寿险公司经济资本研究
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摘要
寿险公司所承担的社会角色和及经营活动都是聚集社会风险同时将其分散化的过程,因此他们天然的对风险管理更为重视。同时公众和政府对保险行业的风险状况也都比较敏感,保险行业一直处于严格的监管之下。对于保险公司的风险评估,从准备金的计算方法到偿付能力的标准都一直处于不断发展变化之中。每个国家也根据自己的实际情况,发展出了各自对保险公司风险的评估方法。目前,在欧美等发达的保险市场,基于经济资本的整体化风险管理框架已经基本被业界接受并且各家公司都在这一原则下开发各自独立的度量风险模型,也即内部模型。而国内的一些公司也在开展相关的研究。
在内部模型中,我们需要合理的评估和度量公司面临的各种风险。本文主要关注我国寿险公司面临的核心风险也即保险风险,提出了采用随机模型的方法来刻画保险风险。文中首先阐述了保险风险并将其分为了三个部分:利率风险,死亡率风险和退保率风险,然后对这三个风险进行了详细的分析和建模。采用时间序列的方法研究了利率模型;在Bayesian框架下提出了采用MCMC的方法来估计传统的Lee-Carter死亡率模型,然后基于中国生命表详细研究了国内寿险公司所面临的死亡率风险;采用广义线性模型的方法分析了退保率风险并考虑了退保率和利率之间的关系。最后阐明了寿险公司如何基于Var和TVar的风险度量方法整体评估应持有的经济资本。
本文详细分析和研究了国内寿险公司所面临的保险风险,对于我国寿险行业偿付能力研究有着一定的实际意义。
The social role of life insurance companies and their operating activities are gathering and diversifying risk at the same time, so they naturally pay more attention to risk management. The public and the government’s attitude on the insurance industry's risk are also very sensitive, and the insurance industry is under strict supervision. Risk assessment for insurance companies, from the valuation of the reserve to the solvency standards have been in continuous development. Each country has developed their own regulation standards on insurance companies according to their actual situation. Currently, the enterprise risk management framework based on the economic capital has been accepted by the industry and various companies in Europe and the United States and other developed insurance market. Each company independently develops their risk measurement models, i.e. the internal model. Some of the domestic companies are also doing related research.
In the internal model, we need to assess and measure various risks faced by companies in a reasonable model. This paper focuses on the core risk of China's life insurance companies faced which is insurance risk, random model are proposed to characterize the insurance risk. The paper firstly described the insurance risk and divided it into three parts: interest rate risk, mortality risk and surrender risk. Then we analyze and model these three risks in detail. Time series method was used to study the interest rate risk model; MCMC method in the Bayesian framework was proposed to estimate the traditional Lee-Carter mortality model, and then the mortality risk faced by the domestic life insurance companies was detailed assessment based on the Chinese life table; generalized linear models was used to analyze the surrender risk and we also consider the relationship of the surrender rate and interest rate. Finally, the economic capital amount was measured based on the VaR and TVaR method in order to against these three risks.
This paper analyzed and studied the life insurance risk faced by the domestic company in detail, and has a certain practical significance to the solvency study of China's life insurance industry.
在内部模型中,我们需要合理的评估和度量公司面临的各种风险。本文主要关注我国寿险公司面临的核心风险也即保险风险,提出了采用随机模型的方法来刻画保险风险。文中首先阐述了保险风险并将其分为了三个部分:利率风险,死亡率风险和退保率风险,然后对这三个风险进行了详细的分析和建模。采用时间序列的方法研究了利率模型;在Bayesian框架下提出了采用MCMC的方法来估计传统的Lee-Carter死亡率模型,然后基于中国生命表详细研究了国内寿险公司所面临的死亡率风险;采用广义线性模型的方法分析了退保率风险并考虑了退保率和利率之间的关系。最后阐明了寿险公司如何基于Var和TVar的风险度量方法整体评估应持有的经济资本。
本文详细分析和研究了国内寿险公司所面临的保险风险,对于我国寿险行业偿付能力研究有着一定的实际意义。
The social role of life insurance companies and their operating activities are gathering and diversifying risk at the same time, so they naturally pay more attention to risk management. The public and the government’s attitude on the insurance industry's risk are also very sensitive, and the insurance industry is under strict supervision. Risk assessment for insurance companies, from the valuation of the reserve to the solvency standards have been in continuous development. Each country has developed their own regulation standards on insurance companies according to their actual situation. Currently, the enterprise risk management framework based on the economic capital has been accepted by the industry and various companies in Europe and the United States and other developed insurance market. Each company independently develops their risk measurement models, i.e. the internal model. Some of the domestic companies are also doing related research.
In the internal model, we need to assess and measure various risks faced by companies in a reasonable model. This paper focuses on the core risk of China's life insurance companies faced which is insurance risk, random model are proposed to characterize the insurance risk. The paper firstly described the insurance risk and divided it into three parts: interest rate risk, mortality risk and surrender risk. Then we analyze and model these three risks in detail. Time series method was used to study the interest rate risk model; MCMC method in the Bayesian framework was proposed to estimate the traditional Lee-Carter mortality model, and then the mortality risk faced by the domestic life insurance companies was detailed assessment based on the Chinese life table; generalized linear models was used to analyze the surrender risk and we also consider the relationship of the surrender rate and interest rate. Finally, the economic capital amount was measured based on the VaR and TVaR method in order to against these three risks.
This paper analyzed and studied the life insurance risk faced by the domestic company in detail, and has a certain practical significance to the solvency study of China's life insurance industry.
引文
陈兵.保险公司偿付能力评估的新视角—经济资本.保险研究, 2006.
陈戈.寿险公司经济资本问题研究.北京:中国商业出版社, 2009.
陈希孺.广义线性模型(一).数理统计与管理, 2002.
李秀芳.我国寿险业的利率风险分析及其防范.南开经济研究, 2001.
魏迎宁,陈戈.论保险公司经济资本.保险研究, 2008.
展凯.中国寿险市场退保影响因素的实证分析.当代经济科学, 2008.
中国保险监督管理委员会.保险公司最低偿付能力及监管指标管理规定(试行). 2001年1月
Ahlgrim, K., D’Arcy, S., & Gorvett, R. Modeling of Economic Series Coordinated with Interest Rate Scenarios, Research report, Casualty Actuarial Society and Society of Actuaries, 2004.
Beelders, Owen and David Colarossi. Modeling Mortality Risk with Extreme Value Theory: The Case of Swiss Re’s Mortality-Indexed Bonds. Global Association of Risk Professionals, 2004.
Bowers, N., H. Gerber, J.Hickman, D. Jones, and C. Nesbitt. Actuarial Mathematics (2nd ed.), Society of Actuaries, 1997.
Brouhns, N., Denuit, M. and Van Keilegom, I. Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scandinavian Actuarial Journal 212–224, 2005.
Brouhns, N., Denuit, M. and Van Keilegom, I. Measuring the longevity risk in mortality projections. Bulletin of the Swiss Association of Actuaries, 2002.
Cairns, A. A multifactor equilibrium model for the term structure and inflation. Proceedings of the 9th International AFIR Colloquium, Tokyo, 1999.
Cairns, A. A discussion of parameter and model uncertainty in insurance. Insurance:Mathematics and Economics, 2000.
Carter, L. Forecasting U.S. mortality: a comparison of Box-Jenkins ARIMA and structural time series models. The Sociological Quarterly, 1995.
Czado, C., Delwarde, A. and Denuit, M. (2005). Bayesian Poisson log-bilinear mortality projections. Insurance: Mathematics & Economics, 2005.
Daykin, C., Pentik?inen, T., and Pesonen, M. Practical Risk Theory for Actuaries, Chapman and Hall, London, 1994.
Frees, E. Stochastic life contingencies with solvency considerations. Transactions of the Society of Actuaries, 1990.
Genevieve Hayes. Stochastic Solvency Testing in Life Insurance. Biennial Convention, Institute of Actuaries of Australia, 2009.
Hastings WK. (1970). Monte Carlo sampling methods using Markov chain and their applications. Biometrika, 1970.
Kim, C. Modeling surrender and lapse rates with economic variables. North American Actuarial Journal, 2005.
Kuo, W., C. Tsai, and W. Chen. An empirical study on the lapse rate: the cointegration approach. Journal of Risk and Insurance, 2003.
Lee, P. A general framework for stochastic investigation of mortality and investment risks. Presented at Wilkiefest, Heriot-Watt University, 2000.
Lee, R.D. The Lee-Carter method of forecasting mortality, with various extensions and applications. North American Actuarial Journal, 2000.
Lee, R.D., and Carter, L. Modelling and forecasting the time series of US mortality.Journal of the American Statistical Association, 1992.
Lee, R. D., and Tuljapurkar, S. Stochastic population forecasts for the United States: beyond high, medium and low. Journal of the American Statistical Association, 1994.
Marceau, E. and P. Gaillardetz. On Life Insurance reserves in a stochastic mortality and interest rates environment. Insurance: Mathmatics and Economics, 1999.
Mckay, M., W.Conover, and R.Beckman. A Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 1979.
Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. (1953). Equation of state calculation by fast computer machines. Journal of Chemical Physics, 1953.
OECD. Financial guarantees required from life assurance concerns( the Buol report). Working party report, Organisation for Economic Co-operation and Development, 1971.
Outreville, J. Whole-life insurance lapse rates and the emergency fund hypothesis. Insurance: Mathematics and Economics, 1990, 257, 367-370.
Panjer, H. and D. Bellhouse. Stochastic modelling of interest rates with applications to life contingencies. Journal of Risk and Insurance, 1980.
Parker, G. Stochastic analysis of the interaction between investment and insurance risks. North American Actuarial Journal, 1997.
Pedroza C. 2006. A Bayesian forecasting model: predicting U.S. male mortality. Biostatistics, 2006.
Pedroza, C. Bayesian hierarchical time series modeling of mortality rates, Ph.D. Thesis, Harvard University,Cambridge, MA,2002.
Ross, S. Simulation ( 4th ed. ). Burlington, Massachusetts: Elsevier Academic Press, 2006.
Tsai, C., W. Kuo, and W. Chen. Early surrender and the distribution of policy reserves. Insurance: Mathematics and Economics, 2004.
Wilkie, A. A stochastic investment model for actuarial use, Transactions of the Faculty of Actuaries, 1986.
Wilkie, A. More on a stochastic asset model for actuarial use, British Actuarial Journal, 1995.
Wilmoth, J. R. (1995). Are mortality projections always more pessimistic when disaggregated by cause of death? Mathematical Population Studies, 1995.
陈戈.寿险公司经济资本问题研究.北京:中国商业出版社, 2009.
陈希孺.广义线性模型(一).数理统计与管理, 2002.
李秀芳.我国寿险业的利率风险分析及其防范.南开经济研究, 2001.
魏迎宁,陈戈.论保险公司经济资本.保险研究, 2008.
展凯.中国寿险市场退保影响因素的实证分析.当代经济科学, 2008.
中国保险监督管理委员会.保险公司最低偿付能力及监管指标管理规定(试行). 2001年1月
Ahlgrim, K., D’Arcy, S., & Gorvett, R. Modeling of Economic Series Coordinated with Interest Rate Scenarios, Research report, Casualty Actuarial Society and Society of Actuaries, 2004.
Beelders, Owen and David Colarossi. Modeling Mortality Risk with Extreme Value Theory: The Case of Swiss Re’s Mortality-Indexed Bonds. Global Association of Risk Professionals, 2004.
Bowers, N., H. Gerber, J.Hickman, D. Jones, and C. Nesbitt. Actuarial Mathematics (2nd ed.), Society of Actuaries, 1997.
Brouhns, N., Denuit, M. and Van Keilegom, I. Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scandinavian Actuarial Journal 212–224, 2005.
Brouhns, N., Denuit, M. and Van Keilegom, I. Measuring the longevity risk in mortality projections. Bulletin of the Swiss Association of Actuaries, 2002.
Cairns, A. A multifactor equilibrium model for the term structure and inflation. Proceedings of the 9th International AFIR Colloquium, Tokyo, 1999.
Cairns, A. A discussion of parameter and model uncertainty in insurance. Insurance:Mathematics and Economics, 2000.
Carter, L. Forecasting U.S. mortality: a comparison of Box-Jenkins ARIMA and structural time series models. The Sociological Quarterly, 1995.
Czado, C., Delwarde, A. and Denuit, M. (2005). Bayesian Poisson log-bilinear mortality projections. Insurance: Mathematics & Economics, 2005.
Daykin, C., Pentik?inen, T., and Pesonen, M. Practical Risk Theory for Actuaries, Chapman and Hall, London, 1994.
Frees, E. Stochastic life contingencies with solvency considerations. Transactions of the Society of Actuaries, 1990.
Genevieve Hayes. Stochastic Solvency Testing in Life Insurance. Biennial Convention, Institute of Actuaries of Australia, 2009.
Hastings WK. (1970). Monte Carlo sampling methods using Markov chain and their applications. Biometrika, 1970.
Kim, C. Modeling surrender and lapse rates with economic variables. North American Actuarial Journal, 2005.
Kuo, W., C. Tsai, and W. Chen. An empirical study on the lapse rate: the cointegration approach. Journal of Risk and Insurance, 2003.
Lee, P. A general framework for stochastic investigation of mortality and investment risks. Presented at Wilkiefest, Heriot-Watt University, 2000.
Lee, R.D. The Lee-Carter method of forecasting mortality, with various extensions and applications. North American Actuarial Journal, 2000.
Lee, R.D., and Carter, L. Modelling and forecasting the time series of US mortality.Journal of the American Statistical Association, 1992.
Lee, R. D., and Tuljapurkar, S. Stochastic population forecasts for the United States: beyond high, medium and low. Journal of the American Statistical Association, 1994.
Marceau, E. and P. Gaillardetz. On Life Insurance reserves in a stochastic mortality and interest rates environment. Insurance: Mathmatics and Economics, 1999.
Mckay, M., W.Conover, and R.Beckman. A Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 1979.
Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. (1953). Equation of state calculation by fast computer machines. Journal of Chemical Physics, 1953.
OECD. Financial guarantees required from life assurance concerns( the Buol report). Working party report, Organisation for Economic Co-operation and Development, 1971.
Outreville, J. Whole-life insurance lapse rates and the emergency fund hypothesis. Insurance: Mathematics and Economics, 1990, 257, 367-370.
Panjer, H. and D. Bellhouse. Stochastic modelling of interest rates with applications to life contingencies. Journal of Risk and Insurance, 1980.
Parker, G. Stochastic analysis of the interaction between investment and insurance risks. North American Actuarial Journal, 1997.
Pedroza C. 2006. A Bayesian forecasting model: predicting U.S. male mortality. Biostatistics, 2006.
Pedroza, C. Bayesian hierarchical time series modeling of mortality rates, Ph.D. Thesis, Harvard University,Cambridge, MA,2002.
Ross, S. Simulation ( 4th ed. ). Burlington, Massachusetts: Elsevier Academic Press, 2006.
Tsai, C., W. Kuo, and W. Chen. Early surrender and the distribution of policy reserves. Insurance: Mathematics and Economics, 2004.
Wilkie, A. A stochastic investment model for actuarial use, Transactions of the Faculty of Actuaries, 1986.
Wilkie, A. More on a stochastic asset model for actuarial use, British Actuarial Journal, 1995.
Wilmoth, J. R. (1995). Are mortality projections always more pessimistic when disaggregated by cause of death? Mathematical Population Studies, 1995.
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