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Abstract and Applied Analysis
Volume 2014, Article ID 194962, 19 pages
http://dx.doi.org/10.1155/2014/194962
Research Article

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

1Department of Mathematics, Tianjin University, Tianjin 300072, China
2Center for Applied Mathematics, Tianjin University, Tianjin 300072, China

Received 18 March 2014; Revised 20 June 2014; Accepted 25 June 2014; Published 24 July 2014

Academic Editor: Simone Marsiglio

Copyright © 2014 De-Lei Sheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.