实物期权与部分信息若干问题研究
|
摘要
本学位论文针对非完备市场中实物期权与部分信息相关的若干问题，运用统计滤波技术、随机控制理论、均衡定价和消费效用无差别定价方法，建立严格的数理金融模型，研究实物期权定价、择时、融资结构的数量规律，给出资产定价和风险对冲对部分信息、特质风险等因素的敏感性分析。
本文研究包括如下几个方面：
（1）扩展经典的实物期权理论。假设不可逆投资项目随机收益流的平均增长率是不可观测的正态随机变量，研究最大化无限生命期内的期望消费折扣总效用的实物期权问题。分别针对自保（self-insurance）模型和对冲模型，得到了关于平均增长率的滤波估计，然后在常绝对风险厌恶（CARA）效用函数下，推导出了相应的投资后收益流的确定性等价价值，以及投资期权的隐含价值和最优投资触发水平所满足的具有自由边界的半闭式偏微分方程系统，结果独立于效用的时间折扣因子。运用有限差分方法，获得了数值解，与完备信息下的结果进行对比，给出了信息价值的测算方法。理论分析和数值结果表明部分信息致使延迟投资，并导致投资期权隐含价值的显著损失，该损失在投资触发水平处达到最大，且随着投资者风险厌恶指数、估计风险、项目收益波动率的增加而提高。结果还表明消费效用无差别定价准则不仅考虑了系统风险溢价、也考虑了非系统风险溢价。但是，投资者的风险态度只有在存在非系统风险时，才会对投资消费决策和资产定价产生影响。
（2）研究了宏观经济条件的随机转换对不可逆投资决策问题的影响。假设不可逆投资项目执行后的收益流不仅依赖于企业自身的收益风险，也依赖于企业所处的外部宏观经济状态（繁荣或萧条）。宏观经济状态服从连续时间的两状态马尔科夫链，并以成倍的形式影响项目投资后收益流的价值。通过最优控制与修正的光滑拟合技术，得到对应于每个宏观经济状态下的投资期权隐含价值以及最优投资时刻的闭式解。数值分析给出了宏观经济条件和贴现率的随机转变以及平均增长率、波动率等参数与最优投资和隐含价值的关系。
（3）基于最大化生存概率准则，研究了实物期权的定价与择时问题。假设投资收益流面临着不可对冲的随机风险，企业的目标是如何通过最优执行该期权来最大化其生存概率。运用随机控制理论，通过求解HJB方程，获得了企业的生存概率，实物期权的投资阈值以及相应的期权隐含价值的闭式解，数值分析给出了生存概率和实物投资随财富总量以及项目波动率的变化规律。结果显示：企业的生存概率随财富的增加而增大，期权价值随财富的增加先增大后减小，同时企业拥有项目投资机会显著增强了企业的生存概率。与经典期权定价理论不同的是，收益流的波动率越大，实物期权的隐含价值越小。
（4）在实物投资框架中，研究了或有可转换债券（CCB）作为一种新型的债务融资工具对公司所起到的作用。公司的项目投资行为作为一种实物期权分别以公司价值最大化和股权价值最大化为目标。通过与普通债券融资相比较，分析了CCB对公司最优投资策略、债务代理成本以及公司最优资本结构的影响机制。数值分析表明在内生的转换法则下，一方面，CCB融资会导致公司过度投资，高杠杆以及较大的代理成本。另一方面，CCB融资有效地降低了破产风险，增加了公司的总价值。特别地，对于外生的转换边界，CCB融资显著的降低了代理成本，并存在唯一的外生转换比率使得代理成本降为最小值零。
（5）将部分信息的问题引入到对冲基金的定价模型中，假设对冲基金的期望收益率不可观测但是已知服从两点分布。基金管理者可以根据可观测的对冲基金的净资产价值动态更新他对期望收益率真值的估计。分析了期望收益率的不确定性对基金管理者的各种薪酬水平和投资者权益价值的影响。结果表明：部分信息对管理费、激励费和投资者权益价值产生了显著的经济学影响。特别地，一个没有进行信息更新，仅仅认为期望回报率是个常数的基金管理者总是低估这些价值，而且往往被低估的程度非常严重。净资产价值越接近高收益线（high-water mark），或者期望回报率的不确定性越大，基金价值被低估的程度越明显。
In this dissertation, we consider several problems origining from real options andpartial information under incomplete markets. Based on statistical filtering, stochasticcontrol, equilibrium pricing and consumption utility indifference pricing approaches,we set up formal models of mathematical finance to quantitatively explore the pricing,timing, and financing of real option, and give the sensitivity analysis of asset pricingand risk hedging to the factors of partial information and idiosyncratic risk.
The studies of this dissertation include the following aspects:
(1) We extend the real options theory. Supposing the mean appreciation rateof cash flows generated by an irreversible investment project is an unobservablenormal random variable, we study the problems of real option where the goal of aninvestor is to maximize expected discounted utility of infinite lifetime consumption.Respectively for a self-insurance model and a hedge model, we get the differentKalman filtering estimations of the mean appreciation rate. Based on ConstantAbsolute Risk Aversion (CARA) utility, we derive the certainty equivalent value ofcash flows after investment, and then obtain a semi-closed-form solution of afree-boundary Partial Differential Equation (PDE) system, which are satisfied by theimplied value and the optimal investment threshold of the option to invest. We showthat the solutions are independent of the utility time-discount rate. We providenumerical results by finite difference method, compare the results with those under afully observable case and propose a method to measure the value of information. Thetheory analysis and numerical calculations show that partial information leads to laterinvestment and a significant loss of the implied value of the real option. The lossreaches the maximum value at the investment threshold and it increases with theinvestor’s risk aversion, estimation risk and project’s volatility, any larger value ofwhich leads to a smller option value and a bigger investment threshold. In addition,the results show that the consumption utility indifference pricing approach takes intoaccount non-systematic risk premium, as well as the systematic risk premium. But, therisk attitude of the investor has impacts on the strategies of investment, consumptionand asset pricing only if the investor is exposed to non-systematic risk.
(2) We study the impact of random conversion of macroeconomic conditions onthe problems of irreversible investment. Suppose the stochastic cash flows after investment not only depend on the enterprise’s income risk, but also depend on thecurrent macroeconomic conditions (boom or recession). The macroeconomicconditions obey a continuous-time Markov chain with two states, and influence thecash flows multiply. Through stochastic control theory and modified smooth fittechnology, we obtain the closed form solutions for the implied value and the optimalinvestment threshold of the real option according to the macroeconomic state. Inaddition, the numerical results present the effects of the random conversion ofmacroeconomic conditions and the discount rate, and the parameters such as meanappreciation rate and volatility on the implied option value and the optimal stopping.
(3) We study the pricing and timing of real option based on the criteria ofmaximizing the probability of survival. The firm with uninsured risk of cash flowsafter investment makes decisions on the exercising of the option so as to maximize thesurvival probability. We derive closed-form solutions for the firm’s survivalprobability, investment threshold and the corresponding implied value of real optionby solving the HJB equation based on the theory of stochastic control. The numericalresults present the effects of wealth and volatility on the survival probability and realinvestment. It shows that the firm’s survival probability increases with wealth and theimplied option value increases firstly and then decreases with the increasing of thewealth. The firm significantly enhances the survival probability due to the investmentopportunity. A strong discover of our study different to the classic option pricingtheory is that the higher the uncertainty of the cash flow, the lower the option value.
(4) We focus on the role of contingent convertible bond (CCB) as a debtfinancing instrument in an investment-based framework. We model the firm’sinvestment behavior as a real option which is exercised under firm-value andequity-value maximizing policies respectively. We attempt to clarify how CCB affectsthe firm’s investment policy, agency cost of debt and optimal capital structure throughcomparing with straight bond financing. Numerical analysis demonstrates that underan endogenous conversion rule, CCB financing leads to overinvestment, a higherleverage and a bigger agency cost. At the same time, CCB financing decreasesbankruptcy risk, and increases the firm’s value. In particular, for an exogenousconversion, the CCB financing considerably decreases the agency cost as well. Thereexists a unique exogenous conversion ratio such that the agency cost reaches theminimum value zero.
(5) Introducing the problem of partial information into the pricing model of thehedge fund. Suppose the expected return rate of a hedge fund is not observable but obey a two-point distribution. The fund manager can dynamically update his beliefabout the true value of the expected return based on the realization of the net assetvalue of the hedge fund. We study the impact of the uncertainty of the expected returnrate on the valuation of the fund manager’s various fees and the investor’s claim. Theresults show that partial information has significant impact on the management fees,performance fees and the claims. Specifically, a non-updating fund manager who justtakes the expected return as a constant always underestimates the values, and moreoften than not, the amount underestimated is significant. The closer the net asset valuegets to the high-water mark or the larger the uncertainty of the expected return is, thebigger the amount underestimated will become.
本文研究包括如下几个方面：
（1）扩展经典的实物期权理论。假设不可逆投资项目随机收益流的平均增长率是不可观测的正态随机变量，研究最大化无限生命期内的期望消费折扣总效用的实物期权问题。分别针对自保（self-insurance）模型和对冲模型，得到了关于平均增长率的滤波估计，然后在常绝对风险厌恶（CARA）效用函数下，推导出了相应的投资后收益流的确定性等价价值，以及投资期权的隐含价值和最优投资触发水平所满足的具有自由边界的半闭式偏微分方程系统，结果独立于效用的时间折扣因子。运用有限差分方法，获得了数值解，与完备信息下的结果进行对比，给出了信息价值的测算方法。理论分析和数值结果表明部分信息致使延迟投资，并导致投资期权隐含价值的显著损失，该损失在投资触发水平处达到最大，且随着投资者风险厌恶指数、估计风险、项目收益波动率的增加而提高。结果还表明消费效用无差别定价准则不仅考虑了系统风险溢价、也考虑了非系统风险溢价。但是，投资者的风险态度只有在存在非系统风险时，才会对投资消费决策和资产定价产生影响。
（2）研究了宏观经济条件的随机转换对不可逆投资决策问题的影响。假设不可逆投资项目执行后的收益流不仅依赖于企业自身的收益风险，也依赖于企业所处的外部宏观经济状态（繁荣或萧条）。宏观经济状态服从连续时间的两状态马尔科夫链，并以成倍的形式影响项目投资后收益流的价值。通过最优控制与修正的光滑拟合技术，得到对应于每个宏观经济状态下的投资期权隐含价值以及最优投资时刻的闭式解。数值分析给出了宏观经济条件和贴现率的随机转变以及平均增长率、波动率等参数与最优投资和隐含价值的关系。
（3）基于最大化生存概率准则，研究了实物期权的定价与择时问题。假设投资收益流面临着不可对冲的随机风险，企业的目标是如何通过最优执行该期权来最大化其生存概率。运用随机控制理论，通过求解HJB方程，获得了企业的生存概率，实物期权的投资阈值以及相应的期权隐含价值的闭式解，数值分析给出了生存概率和实物投资随财富总量以及项目波动率的变化规律。结果显示：企业的生存概率随财富的增加而增大，期权价值随财富的增加先增大后减小，同时企业拥有项目投资机会显著增强了企业的生存概率。与经典期权定价理论不同的是，收益流的波动率越大，实物期权的隐含价值越小。
（4）在实物投资框架中，研究了或有可转换债券（CCB）作为一种新型的债务融资工具对公司所起到的作用。公司的项目投资行为作为一种实物期权分别以公司价值最大化和股权价值最大化为目标。通过与普通债券融资相比较，分析了CCB对公司最优投资策略、债务代理成本以及公司最优资本结构的影响机制。数值分析表明在内生的转换法则下，一方面，CCB融资会导致公司过度投资，高杠杆以及较大的代理成本。另一方面，CCB融资有效地降低了破产风险，增加了公司的总价值。特别地，对于外生的转换边界，CCB融资显著的降低了代理成本，并存在唯一的外生转换比率使得代理成本降为最小值零。
（5）将部分信息的问题引入到对冲基金的定价模型中，假设对冲基金的期望收益率不可观测但是已知服从两点分布。基金管理者可以根据可观测的对冲基金的净资产价值动态更新他对期望收益率真值的估计。分析了期望收益率的不确定性对基金管理者的各种薪酬水平和投资者权益价值的影响。结果表明：部分信息对管理费、激励费和投资者权益价值产生了显著的经济学影响。特别地，一个没有进行信息更新，仅仅认为期望回报率是个常数的基金管理者总是低估这些价值，而且往往被低估的程度非常严重。净资产价值越接近高收益线（high-water mark），或者期望回报率的不确定性越大，基金价值被低估的程度越明显。
In this dissertation, we consider several problems origining from real options andpartial information under incomplete markets. Based on statistical filtering, stochasticcontrol, equilibrium pricing and consumption utility indifference pricing approaches,we set up formal models of mathematical finance to quantitatively explore the pricing,timing, and financing of real option, and give the sensitivity analysis of asset pricingand risk hedging to the factors of partial information and idiosyncratic risk.
The studies of this dissertation include the following aspects:
(1) We extend the real options theory. Supposing the mean appreciation rateof cash flows generated by an irreversible investment project is an unobservablenormal random variable, we study the problems of real option where the goal of aninvestor is to maximize expected discounted utility of infinite lifetime consumption.Respectively for a self-insurance model and a hedge model, we get the differentKalman filtering estimations of the mean appreciation rate. Based on ConstantAbsolute Risk Aversion (CARA) utility, we derive the certainty equivalent value ofcash flows after investment, and then obtain a semi-closed-form solution of afree-boundary Partial Differential Equation (PDE) system, which are satisfied by theimplied value and the optimal investment threshold of the option to invest. We showthat the solutions are independent of the utility time-discount rate. We providenumerical results by finite difference method, compare the results with those under afully observable case and propose a method to measure the value of information. Thetheory analysis and numerical calculations show that partial information leads to laterinvestment and a significant loss of the implied value of the real option. The lossreaches the maximum value at the investment threshold and it increases with theinvestor’s risk aversion, estimation risk and project’s volatility, any larger value ofwhich leads to a smller option value and a bigger investment threshold. In addition,the results show that the consumption utility indifference pricing approach takes intoaccount non-systematic risk premium, as well as the systematic risk premium. But, therisk attitude of the investor has impacts on the strategies of investment, consumptionand asset pricing only if the investor is exposed to non-systematic risk.
(2) We study the impact of random conversion of macroeconomic conditions onthe problems of irreversible investment. Suppose the stochastic cash flows after investment not only depend on the enterprise’s income risk, but also depend on thecurrent macroeconomic conditions (boom or recession). The macroeconomicconditions obey a continuous-time Markov chain with two states, and influence thecash flows multiply. Through stochastic control theory and modified smooth fittechnology, we obtain the closed form solutions for the implied value and the optimalinvestment threshold of the real option according to the macroeconomic state. Inaddition, the numerical results present the effects of the random conversion ofmacroeconomic conditions and the discount rate, and the parameters such as meanappreciation rate and volatility on the implied option value and the optimal stopping.
(3) We study the pricing and timing of real option based on the criteria ofmaximizing the probability of survival. The firm with uninsured risk of cash flowsafter investment makes decisions on the exercising of the option so as to maximize thesurvival probability. We derive closed-form solutions for the firm’s survivalprobability, investment threshold and the corresponding implied value of real optionby solving the HJB equation based on the theory of stochastic control. The numericalresults present the effects of wealth and volatility on the survival probability and realinvestment. It shows that the firm’s survival probability increases with wealth and theimplied option value increases firstly and then decreases with the increasing of thewealth. The firm significantly enhances the survival probability due to the investmentopportunity. A strong discover of our study different to the classic option pricingtheory is that the higher the uncertainty of the cash flow, the lower the option value.
(4) We focus on the role of contingent convertible bond (CCB) as a debtfinancing instrument in an investment-based framework. We model the firm’sinvestment behavior as a real option which is exercised under firm-value andequity-value maximizing policies respectively. We attempt to clarify how CCB affectsthe firm’s investment policy, agency cost of debt and optimal capital structure throughcomparing with straight bond financing. Numerical analysis demonstrates that underan endogenous conversion rule, CCB financing leads to overinvestment, a higherleverage and a bigger agency cost. At the same time, CCB financing decreasesbankruptcy risk, and increases the firm’s value. In particular, for an exogenousconversion, the CCB financing considerably decreases the agency cost as well. Thereexists a unique exogenous conversion ratio such that the agency cost reaches theminimum value zero.
(5) Introducing the problem of partial information into the pricing model of thehedge fund. Suppose the expected return rate of a hedge fund is not observable but obey a two-point distribution. The fund manager can dynamically update his beliefabout the true value of the expected return based on the realization of the net assetvalue of the hedge fund. We study the impact of the uncertainty of the expected returnrate on the valuation of the fund manager’s various fees and the investor’s claim. Theresults show that partial information has significant impact on the management fees,performance fees and the claims. Specifically, a non-updating fund manager who justtakes the expected return as a constant always underestimates the values, and moreoften than not, the amount underestimated is significant. The closer the net asset valuegets to the high-water mark or the larger the uncertainty of the expected return is, thebigger the amount underestimated will become.
引文
[1] Dixit A, Pindyck R. Investment under uncertainty. Princeton University Press,Princeton NJ,1994
[2] Black F, Scholes, M. The Pricing of options and corporate liabilities. TheJournal of Political Economy,1973,81(3):637-654
[3] Brennan M J. The role of learning in dynamic portfolio decisions. EuropeanEconomic Review,1998,1(3):295-305
[4] Rogers L C G. The relaxed investor and parameter uncertainty. Finance andStochastics,2001,5(2):131-154
[5] Merton R. On estimating the expected return on the market: An exploratoryinvestigation. Journal of Financial Economics,1980,8(4):323-362
[6] Liptser R S, Shiryayev A N. Statistics of Random Processes. Springer-Verlag,New York,1977
[7] Miao J J, Wang N. Investment, consumption and hedging under incompletemarkets. Journal of Financial Economics,2007,86(3):608-642
[8] Markowitz H M. Portfolio selection. Journal of Finance,1952,7:77-91
[9] Sharpe W. Capital asset prices: A theory of market equilibrium underconditions of risk. Journal of Finance,1964,19(3):425-442
[10] Lintner J. The valuation of risk assets and the selection of risky investments instock portfolios and capital budgets. Review of Economics and Statistics,1965,47(1):13-37
[11] Ross S A. The arbitrage theory of capital asset pricing. Journal of EcomomicTheory,1976,13(3):341-360
[12] Samuelson P A. Lifetime portfolio selection by dynamic stochasticprogramming. Review of Economic and Statistics,1969,51(3):239-246
[13] Merton R C. An intertemporal capital asset pricing model. Econometrica,1973,41(5):867-887
[14] Black F, Scholes, M. The Pricing of options and corporate liabilities. TheJournal of Political Economy,1973,81(3):637-654
[15] Myers S. Determinants of corporate borrowing. Journal of Financial Economics,1977,5(2):147-152
[16] McDonald R, Siegel D. The value of waiting to invest. Quarterly Journal ofEconomics,1986,101(4):707-727
[17] Myers S C, Majd S. Abandonment value and project life. Advances in Futuresand Options Research,1990,4:1-21
[18] Borison A. Real options analysis: Where are the emperor’s clothes? Journal ofApplied Corporate Finance,2005,17(2):17-31.
[19]齐安甜,张维.企业并购投资的期权特征及经济评价.系统工程,2001,19(5):43-48
[20]胡愈,许红莲,岳意定.基于成长期权的企业并购价值评估方法.系统工程,2006,24(6):97-99
[21]何沐文,刘金兰,高奇特.不确定环境下自然资源开发项目投资评价模型.管理科学学报,2013,16(6):46-55
[22] Harrison J M, Kreps D M. Martingales and arbitrage in multi-period securitiesmarkets. Journal of Economic Theory,1979,20(3):381-408
[23] Kreps D M. Arbitrage and equilibrium in economies with infinitely manycommodities. Journal of Mathematical Economics,1981,8(1):15-35.
[24] Harrison J M, Pliska S R. Martingales and stochastic integrals in the theory ofcontinuous trading. Stochastic Processes and Applications,1981,11(3):215-260
[25] EL Karoui N, Quenez M C. Dynamic programming and pricing of contingentclaims in incomplete markets. SIAM Journal of Control Optimization,1995,33(1):29-66
[26] Schweizer M. Option Hedging for Semimartingales. Stochastic Processes andtheir Applications,1991,37(2):339-363
[27] Schweizer M. Semimartingales and Hedging in Incomplete Markets. Theoryof Probability and its Applications,1993,37(1):169-171
[28] Schweizer M. Risk-Minimizing Hedging Strategies under RestrictedInformation. Mathematical Finance,1994,4(4):327-342
[29] Schweizer M. Variance-Optimal Hedging in Discrete Time. Mathematics ofOperations Research,1995,20(1):1-32.
[30]刘海龙,吴冲锋.非完备市场期权定价的-ε套利方法.预测,2001,20(4):17-19
[31]刘海龙,吴冲锋.期权定价方法综述.管理科学学报,2002,5(2):67-73
[32] Hodges S, Neuberger A. Optimal replication of contingent claims undertransaction costs. Review of Futures Markets,1989,8(2):222-239
[33] Zakamouline V I. European option pricing and hedging with both fixed andproportional transaction costs. Journal of Economic Dynamics and Control,2006,30(1):1-25
[34]叶文忠,杨招军,郑毅.抵押贷款证券的效用无差别定价.中国管理科学,2010,18(4):21-27
[35]罗琰.最优投资与效用无差别定价模型研究:[湖南大学博士学位论文].长沙:湖南大学,2011,81-98
[36] Henderson, V. Valuation of claims on non-tradable asset using utilitymaximization. Mathematical Finance,2002,12(4):351-373
[37] Henderson, V. Valuing the option to invest in an incomplete market.Mathematics and Financial Economics,2007,7(1):103-128
[38] Monoyios M. Performance of utility-based strategies for hedging basis risk.Quantitative Finance,2004,4(3):245–255
[39] Musiela M, Zariphopoulou T. An example of indifference prices underexponential preferences. Finance and Stochastics,2004,8(2):229–239
[40] Davis M H A. Optimal hedging with basis risk, in”From Stochastic Calculusto Mathematical Finance: The Shiryaev Festschrift”(Y. Kabanov R. Lipsterand J. Stoyanov, eds.). Springer,2006
[41] Ewald C, Yang Z J. Utility Based Pricing and Exercising of Real Optionsunder Geometric Mean Reversion and Risk Aversion toward Idiosyncratic Risk.Mathematical Methods of Operations Research,2008,68(1):97-123
[42]林正龙.项目投资定价与择时理论研究:[湖南大学博士学位论文].长沙:湖南大学,2006
[43]林正龙,杨招军.项目投资决策实物期权方法.湖南大学学报,2007,34(4):88-92
[44] Carmona R. Indifference Pricing: Theory and Applications. PrincetonUniversity Press,2008
[45]易昊.不完备市场实物期权消费效用无差别定价:[湖南大学硕士学位论文].长沙:湖南大学,2009
[46]杨金强.非完备市场下企业家的投资与消费问题:[湖南大学博士学位论文].长沙:湖南大学,2011,117-129
[47] Merton R C. Life time portfolio selection under uncertainty: The continuoustime model. Review of Economics and Statistics,1969,51(3):247-257
[48] Merton R C. Optimum consumption and portfolio rules in a continuous timemodel. Journal of Economic Theory,1971,3(4):373-413
[49] Cox J, Huang C. Optimal consumption and portfolio policies when asset pricesfollow a diffusion process. Journal of Economic Theory,1989,49(1):33-83
[50] Karatzas I, Lehoczky J, Sethi S, et al. Explicit solution of a generalconsumption-investment problem. Mathematics of Operations Research,1986,11:261-294
[51] Karatzas I, Lehoczky J, Shreve S. Optimal consumption and portfolio decisionsfor a "small investor" on a finite horizon. SIAM Journal of Control and Optimal,1987,25(6):1557-1586
[52] Karatzas I, Lehoczky J, Shreve S. Existence and uniqueness of multi-agentequilibrium in a stochastic, dynamic consumption/investment model.Mathematics of Operations Research,1990,15(1):80-128
[53] Lions P L. Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. Comm. P.D.E.,1983,8, Part I,1101-1134, Part II,1229-1276
[54] Lions P L, Sznitman A S. Stochastic differential equations with reflectingboundary conditions. Communications on Pure and Applied Mathematics,1984,37(4):511-537
[55] Pardoux E, Peng S. Adapted solution of a backward stochastic differentialequation. Systems&Control Letters,1990,14(1):55-61
[56] Peng S. A general stochastic maximum principle for optimal control diffusions.SIAM Journal of Control and Optimal,1990,28(4):966-979
[57] Crandall M G, Lions P L. Viscosity solutions of Hamilton-Jacobi equations.Transactions of the American Mathematical Society,1983,277(1):1-42
[58] Cameron T A. Individual option prices for climate change mitigation. Journalof Public Economics,2005,89(2-3):283-301.
[59] Wei X, Martin O, Oliver M. Indifference Pricing of Weather Derivatives.American Journal of Agricultural,2008,90(4):979-993
[60] Viscusi W K. Valuing risks of death from terrorism and natural disasters.Journal of Risk and uncertainty,2009,38(3):191-213
[61] Leung T, Sircar R. Accounting for risk aversion, vesting, job termination riskand multiple exercises in valuation of employee stock options. MathematicalFinance,2009a,19(1):99-128
[62] Leung T, Sircar R. Exponential hedging with optimal stopping and applicationto ESO valuation. SIAM Journal of Control and Optimization,2009b,48(3):1422-1451
[63] Leung T, Sircar R, Zariphopoulou T. Forward indifference valuation ofAmerican options. Stochastics An International Journal of Probability andStochastic Processes,2012,84(5-6):741-770.
[64] Oberman A, Zariphopoulou T. Pricing early exercise contracts in incompletemarkets. Computational Management Science,2003,1(1):75-107.
[65]杨招军,易昊,宋丹丹,杨金强.基础资产不可交易条件下欧式期权的消费效用无差别定价.湖南大学学报（自然科学版）,2012,12(39):89-93
[66] Gennotte, G. Optimal portfolio choice under incomplete information. Journalof Finance,1986,41(3),733-746
[67] Lakner P. Utility maximization with partial information. Stochastic processesand their applications,1995,56(2):247-273
[68] Lakner P. Optimal trading strategy for an investor: the case of partialinformation. Stochastic Processes and their Applications,1998,76(1):77-97
[69] Sass J, Haussmann U G. Optimizing the terminal wealth under partialinformation: The drift process as a continuous time Markov chain. Finance andStochastics,2004,8(4):553-577
[70] Xia Y. Learning about predictability: The effect of parameter uncertainty onoptimal dynamic asset allocation. Journal of Finance,2001,56(1):205-246
[71] Yang Z J, Ma C Q. Optimal trading strategy with partial information and thevalue of information: the simplified and generalized models. InternationalJournal of Theoretical and Applied Finance,2001,4(5):759-772
[72] Cvitanic J, Lazrak A, Martellini L, et al. Dynamic portfolio choice withparameter uncertainty and the economic value of analysts’ recommendations.Review of Financial Studies,2006,19(4):1113-1156
[73] Bj rk T, Davis M H A, Landén C. Optimal investment under partialinformation. Mathematical Methods of Operations Research,2010,71(2):371-399
[74] Xia J. Mean-variance portfolio choice: quadratic partial hedging.Mathematical Finance,2005,15(3):533–538
[75] Xiong J, Zhou X Y. Mean-variance portfolio selection under partialinformation. SIAM Journal on Control and Optimization,2007,46(1):156-175
[76] Wang N. Optimal consumption and asset allocation with unknown incomegrowth. Journal of Monetary Economics,2009,56(4):524-534
[77]张维,程功.实物期权方法的信息经济学解释.现代财经-天津财经学院学报,2001,21(1):3-6
[78]陈金龙.实物期权定价与风险对冲方法研究.运筹学学报,2005,9(1):82-88
[79]杨招军.最优投资与衍生资产定价问题研究.湖南大学出版社,2008,53-90
[80]梁铄,唐小我,倪得兵.二维信息不对称下的实物期权投资研究.中国管理科学,2008,16(3):137-144
[81] Décamps J P, Mariotti T, Villeneuve S. Investment timing under incompleteinformation. Mathematics of Operations Research,2005,30(2):472-500
[82] Klein M. Irreversible investment under incomplete information. www.manuelklein.com,2007
[83] Klein M. Comment on "investment timing under incomplete information".Mathematics of Operations Research,2009,34(1):249-254
[84] Monoyios M. Marginal utility-based hedging of claims on non-traded assetswith partial information. http://eprints.maths.ox.ac.uk/723/1/marghedg1.pdf,2008-7-31
[85] Yang J Q, Yang Z J. Consumption utility-based pricing and timing of theoption to invest with partial information. Computational Economics,2012,39(2):195-217
[86]杨金强,杨招军.部分信息下实物期权的定价和风险对冲.中国管理科学,2011,19(4):9-16
[87] Rogers L C G. The relaxed investor and parameter uncertainty. Finance andStochastics,2001,5(2):131-154
[88] Nagai H, Peng S. Risk-sensitive dynamic portfolio optimization with partialinformation on infinite time horizon. The Annals of Applied Probability,2002,12(1):173-195
[89] Leland H E. Corporate debt value, bond covenants and optimal capital structuredecisions. Journal of finance,1994,49(4):1213-1252
[90] Mauer D C, Sarkar S. Real Option, Agency Conflicts, and Optimal CapitalStructure. Journal of Banking&Finance,2005,29(6):1405-1428
[91] Sundaresan S, Wang N. Dynamic investment, capital structure, anddebtoverhang. http://www.nhh.no/Files/Filer/institutter/for/seminars/finance/2008_spring/100408.pdf,2006-12-4
[92] Lyandres E, Zhdanov A. Convertible Debt and Investment Timing. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=884305,2013-3-15
[93] Egami M. A game options approach to the investment problem with convertibledebt financing. Journal of Economic Dynamics&Control,2010,34(8):1456-1470
[94] Yagi K, Takashima R. The impact of convertible debt financing on investmenttiming. Economic Modelling,2012,29(6):2407-2416
[95]刘向华,李楚霖.公司债务与内生破产的实物期权方法分析.管理工程学报,2005,19(1):95-99
[96]简志宏,李楚霖.杠杆公司破产决策:实物期权方法.系统工程理论方法应用,2001,10(4):320-324
[97]简志宏,李楚霖.公司债务重组的实物期权方法研究.管理科学学报,2002,5(5):38-43
[98]刘星,彭程.基于企业投融资决策协同互动的实物期权分析.系统工程,2007,25(4):59-63
[99] Fleming W H, Soner H M. Controlled Markov processes and viscosity solutions.Springer,2006
[100] Krylov N V. Controlled diffusion process. Springer,1980
[101] Friedman M. A Theory of the Consumption Function. Princeton: PrincetonUniversity Press,1957
[102] Hall R E. Stochastic implications of the life cycle-permanent incomehypothesis: Theory and evidence. Journal of Political Economy,1978,91(6):249-265
[103] Gryglewicz S, Huisman K J M, Kort P M. Finite project life and uncertaintyeffects on investment. Journal of Economic Dynamics and Control,2008,32(7):2191-2213
[104] Hackbarth D, Miao J J, Morellec E. Capital structure, credit risk, andmacroeconomic conditions. Journal of Finance Economics,2006,82(3):519-550
[105] Guo X, Zhang Q. Closed-form solutions for perpetual American put optionswith regime switching. SIAM Journal on Applied Mathematics,2004,64(6):2034-2049
[106] Buffington J, Elliott R J. American options with regime switching.International Journal of Theoretical and Applied Finance,2002,5(05):497-514
[107] Guo X. An explicit solution to an optimal stopping problem with regimeswitching. Journal of Applied Probability,2001,38(2):464-481
[108] Guo X, Miao J J, Morellec E. Irreversible investment with regime shifts.Journal of Economic Theory,2005,122(1):37-59
[109] Robert A, Rogers L C G. Option pricing with markov-modulated dynamics.SIAM Journal on Control and Optimization,2006,44(6):2063-2078
[110] Chen H, Miao J J, Wang N. Entrepreneurial finance and nondiversifiable risk.Review of Financial Studies,2010,23(12):4348-4388
[111] Duffie D. Dynamic asset pricing theory. Princeton University Press,2001
[112] Merton R C. Option pricing when the underlying stock returns arediscontinuous. Journal of Financial Economics,1976,3(1):125-144
[113] Ingersoll Jr J E. The Subjective and Objective Evaluation of Incentive StockOptions. The Journal of Business,2006,79(2):453-487
[114] Yang Z J, Zhang H. Optimal capital structure with an equity-for guarantee swap.Economics Letters,2013,118(2):355-359
[115] Lucas R E. Asset Prices in Exchange Economy. Econometrica,1978,46(6):1429-1445
[116] Young V R. Optimal investment strategy to minimize the probability oflifetime ruin. North American Actuarial Journal,2004,8(4):106-236
[117] Bayraktar E, Young V R. Minimizing the probability of lifetime ruin underborrowing constraints. Insurance: Mathematics and Economics,2007,41(1):196-221
[118] Bayraktar E, Hu X Y, Young V R. Minimizing the probability of lifetime ruinunder stochastic volatility. Insurance: Mathematics and Economics,2011,49(2):194-206
[119] Bayraktar E, Young V R. Proving regularity of the minimal probability of ruinvia a game of stopping and control. Finance and Stochastics,2011,15(4):785-818
[120] Luo S. Ruin minimization for insurers with borrowing constraints. NorthAmerican Actuarial Journal,2008,12(2):143-174
[121]罗琰,杨招军.最小化破产概率的最优投资.管理科学学报,2011,14(5):77-85
[122] Browne S. Survival and growth with a liability: Optimal portfolio strategies incontinuous time. Mathematics of Operations Research,1997,22(2):468-493
[123] Yang Z J, Huang L H. Optimal portfolio strategies with a liability andrandom risk: the case of different lending and borrowing rates. Journal ofApplied Mathematics&Computing,2004,15(1-2):109-126
[124]罗琰,杨招军,杨金强.最大化生存概率的投资策略.中国管理科学,2009,17(4):46-52
[125]杨昭君,李致中.债务固定的公司最优生存策略.系统工程理论与实践,2001,9(1):6-11
[126] Merton R. Continuous Time Finance. Blackwell, Massachusetts,1990
[127] Bolton P, Chen H, Wang N. A unified theory of Tobin’s q, corporateinvestment, financing, and risk management. Journal of Finance,2011,66(5):1545-1578
[128] Karlin S, Taylor H M. A Second Course on Stochastic Process. Academic, NewYork,1981
[129] Flannery M. Stabilizing large financial institutions with contingent capitalcertificates. CAREFIN Research Paper,2010
[130] McDonald R L. Contingent capital with a dual price trigger. Journal ofFinancial Stability,2013,9(2):230-241
[131] Sundaresan S, Wang Z Y. On the design of contingent capital with a markettrigger. http://www.cicfconference.org/schedule_files/11_18_1.pdf,2013-01
[132] Metaler A, Reesor R M. Valuation of Contingent Capital Bonds inMerton-Type Structural Models. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1965306,2013-3-6
[133] Albul B, Jaffee D M, Tchistyi A. Contingent convertible bonds andcapitalstructure decisions. http://escholarship.org/uc/item/95821712#page-1,2010-3-26
[134] Barucci E, Del Viva L. Dynamic Capital Structure and the Contingent CapitalOption. Annals of Finance,2013,9(3):337-364
[135] Barucci E, Del Viva L. Countercyclical contingent capital. Journal of Banking&Finance,2012,36(6):1688-1709
[136] Himmelberg C P, Tsyplakov S. Pricing contingent capital bonds: incentivesmatter. http://www.efmaefm.org/0EFMAMEETINGS/EFMA%20ANNUAL%20MEETINGS/2012-Barcelona/papers/EFMA2012_0599_fullpaper.pdf,2012
[137] Pennacchi G. A structural model of contingent bank capital. http://business.illinois.edu/finance/papers/2010/pennacchi.pdf,2010-4-15
[138] Bj rk T. Arbitrage theory in continuous time. Oxford University Press, Oxford,1998
[139] Glasserman P, Nouri B. Contingent capital with a capital-ratio trigger.Management Science,2012,58(10):1816-1833
[140] Jensen M C, Meckling W H. Theory of the firm: Managerial behavior, agencycosts and ownership structure. Journal of Financial Economics,1976,3(4):305-360
[141] Leland H E. Agency costs, risk management, and capital structure. Journal ofFinancial,1998,53(4):1213-1244
[142] Goetzmann W N, Ingersoll J E, Ross S A. High-water marks and hedge fundmanagement contracts. Journal of Finance,2003,58(4):1685-1717
[143] Hervé R. The value of waiting tolearning. http://departamentodeadministracion.itam.mx/workingpapers/option11.pdf,2005-5-6
[144] Ackermann C, Mcenally R, Ravenscraft D. The performance of hedge fundsrisk, return, and incentives. Journal of Finance,1999,54(3):833-874
[145] Elton E J, Gruber M J, Blake C R. Incentive fees and mutual funds. The Journalof Finance,2003,58(2):779-804
[146] Lo A W. Hedge funds, systemic risk and the financial crisis of2007-2008:written testimony for the house oversight committee hearing on hedge funds.http://papers.ssrn.com/sol3/papers.cfm?abstract-id=1301217,2008-11-13
[147] Panageas S, Westerfield M M. High water marks: high risk appetities? convexcompensation, long horizons, and portfolio choice. Journal of Finance,2009,64(1):1-36
[148] Wang H, Wang C. Leverage management. Mathematics and FinancialEconomics,2010,3(3-4):161-183
[149] Lan Y C, Wang N, Yang J Q. The economics of hedge funds. Journal ofFinancial Economics,2013,110(2):300-323
[150] Ackermann C, Mcenally R, Ravenscraft D. The performance of hedge fundsrisk, return, and incentives. Journal of Finance,1999,54(3):833-874
[151] Agarwal V, Naik N Y. Risks and portfolio decisions involving hedge funds.Review of Financial Studies,2004,17(1):63-98
[152] Getmansky M, Lo A W, Makarov I. An econometric model of serial correlationand illiquidity in hedge fund returns. Journal of Financial Economics,2004,74(3):529-609
[153] Rouge R, EI Karoui N. Pricing via utility maximization and entropy.Mathematic Finance,2000,56(4):524-534
[154] Yanenko N N. The method of fractional steps. Springer-Verlag,1971
[155] Karatzas I, Shreve S E. Brownian Motion and Stochastic Calculus. Springer,1991
[156] Judd K. Numerical methods in economics. Mit Press,1998
[2] Black F, Scholes, M. The Pricing of options and corporate liabilities. TheJournal of Political Economy,1973,81(3):637-654
[3] Brennan M J. The role of learning in dynamic portfolio decisions. EuropeanEconomic Review,1998,1(3):295-305
[4] Rogers L C G. The relaxed investor and parameter uncertainty. Finance andStochastics,2001,5(2):131-154
[5] Merton R. On estimating the expected return on the market: An exploratoryinvestigation. Journal of Financial Economics,1980,8(4):323-362
[6] Liptser R S, Shiryayev A N. Statistics of Random Processes. Springer-Verlag,New York,1977
[7] Miao J J, Wang N. Investment, consumption and hedging under incompletemarkets. Journal of Financial Economics,2007,86(3):608-642
[8] Markowitz H M. Portfolio selection. Journal of Finance,1952,7:77-91
[9] Sharpe W. Capital asset prices: A theory of market equilibrium underconditions of risk. Journal of Finance,1964,19(3):425-442
[10] Lintner J. The valuation of risk assets and the selection of risky investments instock portfolios and capital budgets. Review of Economics and Statistics,1965,47(1):13-37
[11] Ross S A. The arbitrage theory of capital asset pricing. Journal of EcomomicTheory,1976,13(3):341-360
[12] Samuelson P A. Lifetime portfolio selection by dynamic stochasticprogramming. Review of Economic and Statistics,1969,51(3):239-246
[13] Merton R C. An intertemporal capital asset pricing model. Econometrica,1973,41(5):867-887
[14] Black F, Scholes, M. The Pricing of options and corporate liabilities. TheJournal of Political Economy,1973,81(3):637-654
[15] Myers S. Determinants of corporate borrowing. Journal of Financial Economics,1977,5(2):147-152
[16] McDonald R, Siegel D. The value of waiting to invest. Quarterly Journal ofEconomics,1986,101(4):707-727
[17] Myers S C, Majd S. Abandonment value and project life. Advances in Futuresand Options Research,1990,4:1-21
[18] Borison A. Real options analysis: Where are the emperor’s clothes? Journal ofApplied Corporate Finance,2005,17(2):17-31.
[19]齐安甜,张维.企业并购投资的期权特征及经济评价.系统工程,2001,19(5):43-48
[20]胡愈,许红莲,岳意定.基于成长期权的企业并购价值评估方法.系统工程,2006,24(6):97-99
[21]何沐文,刘金兰,高奇特.不确定环境下自然资源开发项目投资评价模型.管理科学学报,2013,16(6):46-55
[22] Harrison J M, Kreps D M. Martingales and arbitrage in multi-period securitiesmarkets. Journal of Economic Theory,1979,20(3):381-408
[23] Kreps D M. Arbitrage and equilibrium in economies with infinitely manycommodities. Journal of Mathematical Economics,1981,8(1):15-35.
[24] Harrison J M, Pliska S R. Martingales and stochastic integrals in the theory ofcontinuous trading. Stochastic Processes and Applications,1981,11(3):215-260
[25] EL Karoui N, Quenez M C. Dynamic programming and pricing of contingentclaims in incomplete markets. SIAM Journal of Control Optimization,1995,33(1):29-66
[26] Schweizer M. Option Hedging for Semimartingales. Stochastic Processes andtheir Applications,1991,37(2):339-363
[27] Schweizer M. Semimartingales and Hedging in Incomplete Markets. Theoryof Probability and its Applications,1993,37(1):169-171
[28] Schweizer M. Risk-Minimizing Hedging Strategies under RestrictedInformation. Mathematical Finance,1994,4(4):327-342
[29] Schweizer M. Variance-Optimal Hedging in Discrete Time. Mathematics ofOperations Research,1995,20(1):1-32.
[30]刘海龙,吴冲锋.非完备市场期权定价的-ε套利方法.预测,2001,20(4):17-19
[31]刘海龙,吴冲锋.期权定价方法综述.管理科学学报,2002,5(2):67-73
[32] Hodges S, Neuberger A. Optimal replication of contingent claims undertransaction costs. Review of Futures Markets,1989,8(2):222-239
[33] Zakamouline V I. European option pricing and hedging with both fixed andproportional transaction costs. Journal of Economic Dynamics and Control,2006,30(1):1-25
[34]叶文忠,杨招军,郑毅.抵押贷款证券的效用无差别定价.中国管理科学,2010,18(4):21-27
[35]罗琰.最优投资与效用无差别定价模型研究:[湖南大学博士学位论文].长沙:湖南大学,2011,81-98
[36] Henderson, V. Valuation of claims on non-tradable asset using utilitymaximization. Mathematical Finance,2002,12(4):351-373
[37] Henderson, V. Valuing the option to invest in an incomplete market.Mathematics and Financial Economics,2007,7(1):103-128
[38] Monoyios M. Performance of utility-based strategies for hedging basis risk.Quantitative Finance,2004,4(3):245–255
[39] Musiela M, Zariphopoulou T. An example of indifference prices underexponential preferences. Finance and Stochastics,2004,8(2):229–239
[40] Davis M H A. Optimal hedging with basis risk, in”From Stochastic Calculusto Mathematical Finance: The Shiryaev Festschrift”(Y. Kabanov R. Lipsterand J. Stoyanov, eds.). Springer,2006
[41] Ewald C, Yang Z J. Utility Based Pricing and Exercising of Real Optionsunder Geometric Mean Reversion and Risk Aversion toward Idiosyncratic Risk.Mathematical Methods of Operations Research,2008,68(1):97-123
[42]林正龙.项目投资定价与择时理论研究:[湖南大学博士学位论文].长沙:湖南大学,2006
[43]林正龙,杨招军.项目投资决策实物期权方法.湖南大学学报,2007,34(4):88-92
[44] Carmona R. Indifference Pricing: Theory and Applications. PrincetonUniversity Press,2008
[45]易昊.不完备市场实物期权消费效用无差别定价:[湖南大学硕士学位论文].长沙:湖南大学,2009
[46]杨金强.非完备市场下企业家的投资与消费问题:[湖南大学博士学位论文].长沙:湖南大学,2011,117-129
[47] Merton R C. Life time portfolio selection under uncertainty: The continuoustime model. Review of Economics and Statistics,1969,51(3):247-257
[48] Merton R C. Optimum consumption and portfolio rules in a continuous timemodel. Journal of Economic Theory,1971,3(4):373-413
[49] Cox J, Huang C. Optimal consumption and portfolio policies when asset pricesfollow a diffusion process. Journal of Economic Theory,1989,49(1):33-83
[50] Karatzas I, Lehoczky J, Sethi S, et al. Explicit solution of a generalconsumption-investment problem. Mathematics of Operations Research,1986,11:261-294
[51] Karatzas I, Lehoczky J, Shreve S. Optimal consumption and portfolio decisionsfor a "small investor" on a finite horizon. SIAM Journal of Control and Optimal,1987,25(6):1557-1586
[52] Karatzas I, Lehoczky J, Shreve S. Existence and uniqueness of multi-agentequilibrium in a stochastic, dynamic consumption/investment model.Mathematics of Operations Research,1990,15(1):80-128
[53] Lions P L. Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. Comm. P.D.E.,1983,8, Part I,1101-1134, Part II,1229-1276
[54] Lions P L, Sznitman A S. Stochastic differential equations with reflectingboundary conditions. Communications on Pure and Applied Mathematics,1984,37(4):511-537
[55] Pardoux E, Peng S. Adapted solution of a backward stochastic differentialequation. Systems&Control Letters,1990,14(1):55-61
[56] Peng S. A general stochastic maximum principle for optimal control diffusions.SIAM Journal of Control and Optimal,1990,28(4):966-979
[57] Crandall M G, Lions P L. Viscosity solutions of Hamilton-Jacobi equations.Transactions of the American Mathematical Society,1983,277(1):1-42
[58] Cameron T A. Individual option prices for climate change mitigation. Journalof Public Economics,2005,89(2-3):283-301.
[59] Wei X, Martin O, Oliver M. Indifference Pricing of Weather Derivatives.American Journal of Agricultural,2008,90(4):979-993
[60] Viscusi W K. Valuing risks of death from terrorism and natural disasters.Journal of Risk and uncertainty,2009,38(3):191-213
[61] Leung T, Sircar R. Accounting for risk aversion, vesting, job termination riskand multiple exercises in valuation of employee stock options. MathematicalFinance,2009a,19(1):99-128
[62] Leung T, Sircar R. Exponential hedging with optimal stopping and applicationto ESO valuation. SIAM Journal of Control and Optimization,2009b,48(3):1422-1451
[63] Leung T, Sircar R, Zariphopoulou T. Forward indifference valuation ofAmerican options. Stochastics An International Journal of Probability andStochastic Processes,2012,84(5-6):741-770.
[64] Oberman A, Zariphopoulou T. Pricing early exercise contracts in incompletemarkets. Computational Management Science,2003,1(1):75-107.
[65]杨招军,易昊,宋丹丹,杨金强.基础资产不可交易条件下欧式期权的消费效用无差别定价.湖南大学学报（自然科学版）,2012,12(39):89-93
[66] Gennotte, G. Optimal portfolio choice under incomplete information. Journalof Finance,1986,41(3),733-746
[67] Lakner P. Utility maximization with partial information. Stochastic processesand their applications,1995,56(2):247-273
[68] Lakner P. Optimal trading strategy for an investor: the case of partialinformation. Stochastic Processes and their Applications,1998,76(1):77-97
[69] Sass J, Haussmann U G. Optimizing the terminal wealth under partialinformation: The drift process as a continuous time Markov chain. Finance andStochastics,2004,8(4):553-577
[70] Xia Y. Learning about predictability: The effect of parameter uncertainty onoptimal dynamic asset allocation. Journal of Finance,2001,56(1):205-246
[71] Yang Z J, Ma C Q. Optimal trading strategy with partial information and thevalue of information: the simplified and generalized models. InternationalJournal of Theoretical and Applied Finance,2001,4(5):759-772
[72] Cvitanic J, Lazrak A, Martellini L, et al. Dynamic portfolio choice withparameter uncertainty and the economic value of analysts’ recommendations.Review of Financial Studies,2006,19(4):1113-1156
[73] Bj rk T, Davis M H A, Landén C. Optimal investment under partialinformation. Mathematical Methods of Operations Research,2010,71(2):371-399
[74] Xia J. Mean-variance portfolio choice: quadratic partial hedging.Mathematical Finance,2005,15(3):533–538
[75] Xiong J, Zhou X Y. Mean-variance portfolio selection under partialinformation. SIAM Journal on Control and Optimization,2007,46(1):156-175
[76] Wang N. Optimal consumption and asset allocation with unknown incomegrowth. Journal of Monetary Economics,2009,56(4):524-534
[77]张维,程功.实物期权方法的信息经济学解释.现代财经-天津财经学院学报,2001,21(1):3-6
[78]陈金龙.实物期权定价与风险对冲方法研究.运筹学学报,2005,9(1):82-88
[79]杨招军.最优投资与衍生资产定价问题研究.湖南大学出版社,2008,53-90
[80]梁铄,唐小我,倪得兵.二维信息不对称下的实物期权投资研究.中国管理科学,2008,16(3):137-144
[81] Décamps J P, Mariotti T, Villeneuve S. Investment timing under incompleteinformation. Mathematics of Operations Research,2005,30(2):472-500
[82] Klein M. Irreversible investment under incomplete information. www.manuelklein.com,2007
[83] Klein M. Comment on "investment timing under incomplete information".Mathematics of Operations Research,2009,34(1):249-254
[84] Monoyios M. Marginal utility-based hedging of claims on non-traded assetswith partial information. http://eprints.maths.ox.ac.uk/723/1/marghedg1.pdf,2008-7-31
[85] Yang J Q, Yang Z J. Consumption utility-based pricing and timing of theoption to invest with partial information. Computational Economics,2012,39(2):195-217
[86]杨金强,杨招军.部分信息下实物期权的定价和风险对冲.中国管理科学,2011,19(4):9-16
[87] Rogers L C G. The relaxed investor and parameter uncertainty. Finance andStochastics,2001,5(2):131-154
[88] Nagai H, Peng S. Risk-sensitive dynamic portfolio optimization with partialinformation on infinite time horizon. The Annals of Applied Probability,2002,12(1):173-195
[89] Leland H E. Corporate debt value, bond covenants and optimal capital structuredecisions. Journal of finance,1994,49(4):1213-1252
[90] Mauer D C, Sarkar S. Real Option, Agency Conflicts, and Optimal CapitalStructure. Journal of Banking&Finance,2005,29(6):1405-1428
[91] Sundaresan S, Wang N. Dynamic investment, capital structure, anddebtoverhang. http://www.nhh.no/Files/Filer/institutter/for/seminars/finance/2008_spring/100408.pdf,2006-12-4
[92] Lyandres E, Zhdanov A. Convertible Debt and Investment Timing. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=884305,2013-3-15
[93] Egami M. A game options approach to the investment problem with convertibledebt financing. Journal of Economic Dynamics&Control,2010,34(8):1456-1470
[94] Yagi K, Takashima R. The impact of convertible debt financing on investmenttiming. Economic Modelling,2012,29(6):2407-2416
[95]刘向华,李楚霖.公司债务与内生破产的实物期权方法分析.管理工程学报,2005,19(1):95-99
[96]简志宏,李楚霖.杠杆公司破产决策:实物期权方法.系统工程理论方法应用,2001,10(4):320-324
[97]简志宏,李楚霖.公司债务重组的实物期权方法研究.管理科学学报,2002,5(5):38-43
[98]刘星,彭程.基于企业投融资决策协同互动的实物期权分析.系统工程,2007,25(4):59-63
[99] Fleming W H, Soner H M. Controlled Markov processes and viscosity solutions.Springer,2006
[100] Krylov N V. Controlled diffusion process. Springer,1980
[101] Friedman M. A Theory of the Consumption Function. Princeton: PrincetonUniversity Press,1957
[102] Hall R E. Stochastic implications of the life cycle-permanent incomehypothesis: Theory and evidence. Journal of Political Economy,1978,91(6):249-265
[103] Gryglewicz S, Huisman K J M, Kort P M. Finite project life and uncertaintyeffects on investment. Journal of Economic Dynamics and Control,2008,32(7):2191-2213
[104] Hackbarth D, Miao J J, Morellec E. Capital structure, credit risk, andmacroeconomic conditions. Journal of Finance Economics,2006,82(3):519-550
[105] Guo X, Zhang Q. Closed-form solutions for perpetual American put optionswith regime switching. SIAM Journal on Applied Mathematics,2004,64(6):2034-2049
[106] Buffington J, Elliott R J. American options with regime switching.International Journal of Theoretical and Applied Finance,2002,5(05):497-514
[107] Guo X. An explicit solution to an optimal stopping problem with regimeswitching. Journal of Applied Probability,2001,38(2):464-481
[108] Guo X, Miao J J, Morellec E. Irreversible investment with regime shifts.Journal of Economic Theory,2005,122(1):37-59
[109] Robert A, Rogers L C G. Option pricing with markov-modulated dynamics.SIAM Journal on Control and Optimization,2006,44(6):2063-2078
[110] Chen H, Miao J J, Wang N. Entrepreneurial finance and nondiversifiable risk.Review of Financial Studies,2010,23(12):4348-4388
[111] Duffie D. Dynamic asset pricing theory. Princeton University Press,2001
[112] Merton R C. Option pricing when the underlying stock returns arediscontinuous. Journal of Financial Economics,1976,3(1):125-144
[113] Ingersoll Jr J E. The Subjective and Objective Evaluation of Incentive StockOptions. The Journal of Business,2006,79(2):453-487
[114] Yang Z J, Zhang H. Optimal capital structure with an equity-for guarantee swap.Economics Letters,2013,118(2):355-359
[115] Lucas R E. Asset Prices in Exchange Economy. Econometrica,1978,46(6):1429-1445
[116] Young V R. Optimal investment strategy to minimize the probability oflifetime ruin. North American Actuarial Journal,2004,8(4):106-236
[117] Bayraktar E, Young V R. Minimizing the probability of lifetime ruin underborrowing constraints. Insurance: Mathematics and Economics,2007,41(1):196-221
[118] Bayraktar E, Hu X Y, Young V R. Minimizing the probability of lifetime ruinunder stochastic volatility. Insurance: Mathematics and Economics,2011,49(2):194-206
[119] Bayraktar E, Young V R. Proving regularity of the minimal probability of ruinvia a game of stopping and control. Finance and Stochastics,2011,15(4):785-818
[120] Luo S. Ruin minimization for insurers with borrowing constraints. NorthAmerican Actuarial Journal,2008,12(2):143-174
[121]罗琰,杨招军.最小化破产概率的最优投资.管理科学学报,2011,14(5):77-85
[122] Browne S. Survival and growth with a liability: Optimal portfolio strategies incontinuous time. Mathematics of Operations Research,1997,22(2):468-493
[123] Yang Z J, Huang L H. Optimal portfolio strategies with a liability andrandom risk: the case of different lending and borrowing rates. Journal ofApplied Mathematics&Computing,2004,15(1-2):109-126
[124]罗琰,杨招军,杨金强.最大化生存概率的投资策略.中国管理科学,2009,17(4):46-52
[125]杨昭君,李致中.债务固定的公司最优生存策略.系统工程理论与实践,2001,9(1):6-11
[126] Merton R. Continuous Time Finance. Blackwell, Massachusetts,1990
[127] Bolton P, Chen H, Wang N. A unified theory of Tobin’s q, corporateinvestment, financing, and risk management. Journal of Finance,2011,66(5):1545-1578
[128] Karlin S, Taylor H M. A Second Course on Stochastic Process. Academic, NewYork,1981
[129] Flannery M. Stabilizing large financial institutions with contingent capitalcertificates. CAREFIN Research Paper,2010
[130] McDonald R L. Contingent capital with a dual price trigger. Journal ofFinancial Stability,2013,9(2):230-241
[131] Sundaresan S, Wang Z Y. On the design of contingent capital with a markettrigger. http://www.cicfconference.org/schedule_files/11_18_1.pdf,2013-01
[132] Metaler A, Reesor R M. Valuation of Contingent Capital Bonds inMerton-Type Structural Models. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1965306,2013-3-6
[133] Albul B, Jaffee D M, Tchistyi A. Contingent convertible bonds andcapitalstructure decisions. http://escholarship.org/uc/item/95821712#page-1,2010-3-26
[134] Barucci E, Del Viva L. Dynamic Capital Structure and the Contingent CapitalOption. Annals of Finance,2013,9(3):337-364
[135] Barucci E, Del Viva L. Countercyclical contingent capital. Journal of Banking&Finance,2012,36(6):1688-1709
[136] Himmelberg C P, Tsyplakov S. Pricing contingent capital bonds: incentivesmatter. http://www.efmaefm.org/0EFMAMEETINGS/EFMA%20ANNUAL%20MEETINGS/2012-Barcelona/papers/EFMA2012_0599_fullpaper.pdf,2012
[137] Pennacchi G. A structural model of contingent bank capital. http://business.illinois.edu/finance/papers/2010/pennacchi.pdf,2010-4-15
[138] Bj rk T. Arbitrage theory in continuous time. Oxford University Press, Oxford,1998
[139] Glasserman P, Nouri B. Contingent capital with a capital-ratio trigger.Management Science,2012,58(10):1816-1833
[140] Jensen M C, Meckling W H. Theory of the firm: Managerial behavior, agencycosts and ownership structure. Journal of Financial Economics,1976,3(4):305-360
[141] Leland H E. Agency costs, risk management, and capital structure. Journal ofFinancial,1998,53(4):1213-1244
[142] Goetzmann W N, Ingersoll J E, Ross S A. High-water marks and hedge fundmanagement contracts. Journal of Finance,2003,58(4):1685-1717
[143] Hervé R. The value of waiting tolearning. http://departamentodeadministracion.itam.mx/workingpapers/option11.pdf,2005-5-6
[144] Ackermann C, Mcenally R, Ravenscraft D. The performance of hedge fundsrisk, return, and incentives. Journal of Finance,1999,54(3):833-874
[145] Elton E J, Gruber M J, Blake C R. Incentive fees and mutual funds. The Journalof Finance,2003,58(2):779-804
[146] Lo A W. Hedge funds, systemic risk and the financial crisis of2007-2008:written testimony for the house oversight committee hearing on hedge funds.http://papers.ssrn.com/sol3/papers.cfm?abstract-id=1301217,2008-11-13
[147] Panageas S, Westerfield M M. High water marks: high risk appetities? convexcompensation, long horizons, and portfolio choice. Journal of Finance,2009,64(1):1-36
[148] Wang H, Wang C. Leverage management. Mathematics and FinancialEconomics,2010,3(3-4):161-183
[149] Lan Y C, Wang N, Yang J Q. The economics of hedge funds. Journal ofFinancial Economics,2013,110(2):300-323
[150] Ackermann C, Mcenally R, Ravenscraft D. The performance of hedge fundsrisk, return, and incentives. Journal of Finance,1999,54(3):833-874
[151] Agarwal V, Naik N Y. Risks and portfolio decisions involving hedge funds.Review of Financial Studies,2004,17(1):63-98
[152] Getmansky M, Lo A W, Makarov I. An econometric model of serial correlationand illiquidity in hedge fund returns. Journal of Financial Economics,2004,74(3):529-609
[153] Rouge R, EI Karoui N. Pricing via utility maximization and entropy.Mathematic Finance,2000,56(4):524-534
[154] Yanenko N N. The method of fractional steps. Springer-Verlag,1971
[155] Karatzas I, Shreve S E. Brownian Motion and Stochastic Calculus. Springer,1991
[156] Judd K. Numerical methods in economics. Mit Press,1998