Optimal investment for insurers with correlation risk: risk aversion and investment horizon

This article investigates the optimal investment for insurers with correlation risk, with the variance-covariance matrix among risky financial assets evolving as a stochastic positive definite matrix process. Using the Wishart diffusion matrix process, we formulate the insurer's investment problem as the maximization of the expected constant relative risk-averse utility function subject to stochastic correlation, stochastic volatilities, and Poisson shocks. We obtain the explicit closed-form investment strategy and optimal expected utility through the Hamilton-Jacobi-Bellman framework. A verification theorem is derived to prove the uniform integrability of a tight upper bound for the objective function. The economic implication is that a long-term stable optimal investment policy requires the insurer to maintain a high risk-aversion level when the financial market contains stochastic volatility and/or stochastic correlation.