OPTIMAL REINSURANCE-INVESTMENT STRATEGIES FOR INSURERS UNDER MEAN-CAR CRITERIA

This paper considers an optimal reinsurance-investment problem for an insurer, who aims to minimize the risk measured by Capital-at-Risk (CaR) with the constraint that the expected terminal wealth is not less than a predefined level. The surplus of the insurer is described by a Brownian motion with drift. The insurer can control her/his risk by purchasing proportional reinsurance, acquiring new business, and investing her/his surplus in a financial market consisting of one risk-free asset and multiple risky assets. Three mean-CaR models are constructed. By transforming these models into bilevel optimization problems, we derive the explicit expressions of the optimal deterministic rebalance reinsurance-investment strategies and the mean-CaR efficient frontiers. Sensitivity analysis of the results and a numerical example are provided.