Optimal decision on dynamic insurance price and investment portfolio of an insurer

We establish a model of insurance pricing with the assumption that the insurance price, insurer investment returns, and insured losses are correlated stochastic processes. We consider the effect of demand on price where the objective of the pricing model is to maximize the expected utility of the insurer’s terminal wealth. Based on a Hamilton–Jacobi–Bellman (HJB) equation, we simultaneously solve for the optimal price of an insurance contract and the optimal investment portfolio of an insurer. The results show that quantity demanded of insurance contracts affects the optimal allocation to risky assets in the insurer’s investment portfolio. Our results also show that the drift and volatility of the insurance price process will affect the investment strategy, in addition to the effect of the drift and volatility of the investment process itself.