| In the study of financial market, Brownian motion has been widely used as the model for the price of risky security. However, some empirical studies of the price of risky security indicate the defects of Brownian motion. Thus, the random impulsive model for stock prices is used to depict the price of risky security.On the other hand, when a dynamic reinsurance policy is incorporated with a dynamic investment strategy in an insurer's business, optimal dynamic choices of reinsurance and investment for insurers is a complicated problem. In this paper an insurer is assumed to invest his reserve in a financial market, which consists of a risky asset and a risk-free asset, to add his wealth while using reinsurance retentions to reduce his risk. The random impulsive model for stock prices is used to depict the price of risky security. A controlled diffusion risk process is presented to describe such a dynamic setting. Explicit and closed-form solutions for the optimal dynamic choice are derived when excess-of-loss or proportional reinsurance is incorporated with an investment under the optimization criteria of maximizing the expectation of quadratic utility of the terminal wealth at a fixed terminal time, respectively. Based on the explicit solutions, the influence of the dependence between the finance risk and insurance risk on the optimal dynamic choice is illustrated numerically. The results shows that the higher the correlation of the finance risk and insurance is, the less the risky investment amount and retention level should be. |
