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Optimal policies for discrete time risk processes with a Markov chain investment model

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  • Diasparra, Maikol
  • Romera, Rosario

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.

Suggested Citation

  • Diasparra, Maikol & Romera, Rosario, 2006. "Optimal policies for discrete time risk processes with a Markov chain investment model," DES - Working Papers. Statistics and Econometrics. WS ws062408, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws062408
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    References listed on IDEAS

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    2. 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.
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    8. Dickson, D. C. M., 2001. "Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)," British Actuarial Journal, Cambridge University Press, vol. 7(4), pages 690-691, October.
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