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Optimal Policies For Discrete Time Risk Processes With A Markov Chain Investment Model

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  • Maikol Diasparra

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  • Rosario Romera

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    Abstract

    We consider a discrete risk process modelled by a Markov Decision Process. The surplus could be invested in stock market assets. We adopt a realistic point of view and we let the investment return process to be statistically dependent over time. We assume that follows a Markov Chain model. To minimize the risk there is a possibility to reinsure a part or the whole reserve. We consider proportional reinsurance. Recursive and integral equations for the ruin probability are given. Generalized Lundberg inequalities for the ruin probabilities are derived. Stochastic optimal control theory is used to determine the optimal stationary policy which minimizes the ruin probability. To illustrate these results numerical examples are included.

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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws062408.

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    Date of creation: May 2006
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    Handle: RePEc:cte:wsrepe:ws062408

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    1. Cai, Jun & Dickson, David C.M., 2004. "Ruin probabilities with a Markov chain interest model," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 513-525, December.
    2. Hipp, Christian & Taksar, Michael, 2000. "Stochastic control for optimal new business," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 185-192, May.
    3. Hipp, Christian & Plum, Michael, 2000. "Optimal investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 215-228, October.
    4. Groniowska, Agnieszka & Niemiro, Wojciech, 2005. "Controlled risk processes in discrete time: Lower and upper approximations to the optimal probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 433-440, June.
    5. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    6. Gajek, Leslaw, 2005. "On the deficit distribution when ruin occurs--discrete time model," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 13-24, February.
    7. Sundt, Bjorn & Teugels, Jozef L., 1995. "Ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 7-22, April.
    8. Sundt, Bjorn & Teugels, Jozef L., 1997. "The adjustment function in ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 19(2), pages 85-94, April.
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