Optimal Decision on Dynamic Insurance Price and Investment Portfolio of An Insurer with Multi-Dimensional Time-Varying Correlation

Abstract

In this article, a model of optimal insurance pricing and investment strategies is established. The insurance price, investment returns and insured losses are assumed to be correlated stochastic processes. N kinds of invested risky assets following multi-Vasicek model with time-varying correlation are discussed in the investment portfolio. Demand of insurance contracts is considered to affect the price of the contracts. The utility is a performance process and is specified for time t and t is equal to or greater than zero. Dynamical optimal price of an insurance contract and the optimal investment portfolio of an insurer are found simultaneously by maximizing the performance of the insurer. Finally, numerical analysis is carried out with an example. The results show that Treasure Bills, generally considered as a risk-free asset, has been examined to follow the similar pattern as other risky assets in the long run; multi-Vasicek model is an appropriate model to describe the change pattern of the return of risky assets invested. The sensitivity of the change of important parameters on the optimal solutions is analyzed. Particularly, the equally weighted investment portfolio can be an optimal investment strategy under some conditions. The proposed model in this paper can be used to obtain optimal solutions easily even in the situation of high dimensional investment portfolio.