Insurance pricing, reinsurance and investment decision based on the Mutual Benefit of the insurer and the customer

In this article, we establish an optimal decision model of insurance pricing, reinsurance and investment based on the mutual benefits of the insurer and the customer instead of only considering the benefit of the insurer, which is conformed with one of important objective of financial institution, that is, customer-oriented. We assume that the price and the claim loss rate are independent stochastic processes and n kinds risky assets are correlated stochastic processes. The main objective of our model is to minimize the expected utility of the premium paid by the customer in a bounded horizon and to maximize the utility of the relative terminal wealth of the insurer respect to the price of insurance. We construct a HJB equation and determine the optimal price of the insurance products, the optimal reinsurance strategy and the optimal investment portfolio of the insurer simultaneously by solving Hamilton-Jacobobi-Bellman HJB equation. Finally, we use an example to illustrate its application.