Optimal proportional reinsurance and investment problem with jump-diffusion risk process under effect of inside information

Abstract

We study optimal investment and proportional reinsurance strategy in the presence of inside information. The risk process is assumed to follow a compound Poisson process perturbed by a standard Brownian motion. The insurer is allowed to invest in a risk-free asset and a risky asset as well as to purchase proportional reinsurance. In addition, it has some extra information available from the beginning of the trading interval, thus introducing in this way inside information aspects to our model. We consider two optimization problems: the problem of maximizing the expected exponential utility of terminal wealth with and without inside information, respectively. By solving the corresponding Hamilton-Jacobi-Bellman equations, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. Finally, we discuss the effects of parameters on the optimal strategy and the effect of the inside information by numerical simulations.