Equilibrium investment–reinsurance strategy under information asymmetry and random horizon

Abstract

This paper investigates an investment–reinsurance problem incorporating information asymmetry and random horizon. At the beginning of the transaction, the insurer owns some inside information related to the risky asset price and the insurance claims. Simultaneously, the return rate and the driving noise for the risky asset process cannot be observed directly. Moreover, the trading horizon is random due to some exogenous factors. Under the dynamic mean–variance criterion, the equilibrium feedback strategy and the associated equilibrium value function are derived in closed form by solving the extended Hamilton–Jacobi–Bellman (HJB) equations. Several special cases are further discussed. Finally, numerical simulations are conducted to analyze the influences of some important parameters on the equilibrium strategy and the efficient frontier.