On the Optimal Dividend Problem for Insurance Risk Models with Surplus-Dependent Premiums

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• 作者：Ewa Marciniak ; Zbigniew Palmowski
• 关键词：Optimal strategy ; PDMP ; Barrier strategy ; Integro ; differential HJB equation ; Gerber–Shiu function ; Stochastic controls ; 60G51 ; 60G50 ; 60K25 ; 93E20
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：168
• 期：2
• 页码：723-742
• 全文大小：491 KB
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• 作者单位：Ewa Marciniak (1)
  Zbigniew Palmowski (2)
  
  1. AGH University of Science and Technology, Kraków, Poland
  2. University of Wrocław, Wrocław, Poland
  
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

This paper concerns an optimal dividend distribution problem for an insurance company with surplus-dependent premium. In the absence of dividend payments, such a risk process is a particular case of so-called piecewise deterministic Markov processes. The control mechanism chooses the size of dividend payments. The objective consists in maximizing the sum of the expected cumulative discounted dividend payments received until the time of ruin and a penalty payment at the time of ruin, which is an increasing function of the size of the shortfall at ruin. A complete solution is presented to the corresponding stochastic control problem. We identify the associated Hamilton–Jacobi–Bellman equation and find necessary and sufficient conditions for optimality of a single dividend-band strategy, in terms of particular Gerber–Shiu functions. A number of concrete examples are analyzed. Keywords Optimal strategy PDMP Barrier strategy Integro-differential HJB equation Gerber–Shiu function Stochastic controls