Risk Management Strategies in a Dependent Perturbed Compound Poisson Model

Abstract

This paper deals with the optimal risk management strategies for an insurer with a diffusion approximation of dependent compound Poisson process who wants to maximize the expected utility by purchasing proportional reinsurance and managing reinsurance counterparty risk with investment and he/she can invest in the financial market and in a risky asset such as stocks. It is assumed that this dependent risk model consists of the constant reinsurance premium rate, combination of the number of claims occurring by policyholders within a finite time, and perturbed by correlated standard Brownian motions, where the price of the risk-free bond is described by a stochastic differential equation. We use the alternative real measure technique to derive the opti-mal strategies and solution of the associated Hamilton-Jacobi-Bellman equation for the optimization problem which is formed by the expectation of combination of financial market factors and an exponential utility function. We prove the verification theorem to guarantee the optimal strategy. Finally, some numerical illustrations are presented to analyze our theoretical results and investigate the sensitivity of optimal strategies on some parameters.