June 2014 Optimal dynamic risk control for insurers with state-dependent income
Ming Zhou, Jun Cai
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J. Appl. Probab. 51(2): 417-435 (June 2014). DOI: 10.1239/jap/1402578634

Abstract

In this paper we investigate optimal forms of dynamic reinsurance polices among a class of general reinsurance strategies. The original surplus process of an insurance portfolio is assumed to follow a Markov jump process with state-dependent income. We assume that the insurer uses a dynamic reinsurance policy to minimize the probability of absolute ruin, where the traditional ruin can be viewed as a special case of absolute ruin. In terms of approximation theory of stochastic process, the controlled diffusion model with a general reinsurance policy is established strictly. In such a risk model, absolute ruin is said to occur when the drift coefficient of the surplus process turns negative, when the insurer has no profitability any more. Under the expected value premium principle, we rigorously prove that a dynamic excess-of-loss reinsurance is the optimal form of reinsurance among a class of general reinsurance strategies in a dynamic control framework. Moreover, by solving the Hamilton-Jacobi-Bellman equation, we derive both the explicit expression of the optimal dynamic excess-of-loss reinsurance strategy and the closed-form solution to the absolute ruin probability under the optimal reinsurance strategy. We also illustrate these explicit solutions using numerical examples.

Citation

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Ming Zhou. Jun Cai. "Optimal dynamic risk control for insurers with state-dependent income." J. Appl. Probab. 51 (2) 417 - 435, June 2014. https://doi.org/10.1239/jap/1402578634

Information

Published: June 2014
First available in Project Euclid: 12 June 2014

zbMATH: 1291.93334
MathSciNet: MR3217776
Digital Object Identifier: 10.1239/jap/1402578634

Subjects:
Primary: 93E20
Secondary: 60H30 , 91B30 , 91B70

Keywords: absolute ruin , excess-of-loss reinsurance , HJB equation , liquid reserve , state-dependent income

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 2 • June 2014
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