ابوذر بازیاری

In this paper, the optimization problems of the terminal wealth of two dependent insurance companies which each of them tries to perform better relative to its competitor is presented. It is assumed that both insurers having the compound Poisson process and they are allowed to purchase proportional reinsurance with a constant reinsurance premium and invest in a financial market which consists of a risk-free asset, a defaultable coupon bond whose the price process of each insurer is governed by a standard Brownian motion and dynamics of defaultable price process is modeled as a mixture of the exponential stochastic differential equation of corporate coupon bonds. For the correlated competing insurance companies, by applying the Girsanov’s theorem and compensated Poisson process, we formulate the wealth process of each insurer based on the reinsurance and investment strategies. By solving the nonlinear Hamilton-Jacobi-Bellman equations related to our optimal control problems with exponential utility functions, the optimal investment and reinsurance strategies are derived for both insurers among all admissible policies. Finally, the influence of each model parameters on the optimal portfolio strategies are discussed by numerical experiments.