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Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions

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  • De-Lei Sheng
  • Ximin Rong
  • Hui Zhao

Abstract

This paper investigates the excess-of-loss reinsurance and investment problem for a compound Poisson jump-diffusion risk process, with the risk asset price modeled by a constant elasticity of variance (CEV) model. It aims at obtaining the explicit optimal control strategy and the optimal value function. Applying stochastic control technique of jump diffusion, a Hamilton-Jacobi-Bellman (HJB) equation is established. Moreover, we show that a closed-form solution for the HJB equation can be found by maximizing the insurer’s exponential utility of terminal wealth with the independence of two Brownian motions and . A verification theorem is also proved to verify that the solution of HJB equation is indeed a solution of this optimal control problem. Then, we quantitatively analyze the effect of different parameter impacts on optimal control strategy and the optimal value function, which show that optimal control strategy is decreasing with the initial wealth and decreasing with the volatility rate of risk asset price. However, the optimal value function is increasing with the appreciation rate of risk asset.

Suggested Citation

  • De-Lei Sheng & Ximin Rong & Hui Zhao, 2014. "Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-19, July.
  • Handle: RePEc:hin:jnlaaa:194962
    DOI: 10.1155/2014/194962
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    Cited by:

    1. Hiroaki Hata & Shuenn-Jyi Sheu & Li-Hsien Sun, 2019. "Expected exponential utility maximization of insurers with a general diffusion factor model : The complete market case," Papers 1903.08957, arXiv.org.
    2. Brachetta, M. & Ceci, C., 2019. "Optimal proportional reinsurance and investment for stochastic factor models," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 15-33.
    3. Matteo Brachetta & Claudia Ceci, 2019. "Optimal excess-of-loss reinsurance for stochastic factor risk models," Papers 1904.05422, arXiv.org.

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