Optimal investment-reinsurance policy for an insurance company with VaR constraint |
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Authors: | Shumin Chen Kemian Li |
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Institution: | a Department of Mathematics Science, School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, PR Chinab Department of Risk Management and Insurance, Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275, PR China |
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Abstract: | This paper investigates an investment-reinsurance problem for an insurance company that has a possibility to choose among different business activities, including reinsurance/new business and security investment. Our main objective is to find the optimal policy to minimize its probability of ruin. The main novelty of this paper is the introduction of a dynamic Value-at-Risk (VaR) constraint. This provides a way to control risk and to fulfill the requirement of regulators on market risk. This problem is formulated as an infinite horizontal stochastic control problem with a constrained control space. The dynamic programming technique is applied to derive the Hamilton-Jacobi-Bellman (HJB) equation and the Lagrange multiplier method is used to tackle the dynamic VaR constraint. Closed-form expressions for the minimal ruin probability as well as the optimal investment-reinsurance/new business policy are derived. It turns out that the risk exposure of the insurance company subject to the dynamic VaR constraint is always lower than otherwise. Finally, a numerical example is given to illustrate our results. |
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Keywords: | Investment-reinsurance Ruin probability Value-at-risk HJB equation Lagrangian method |
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