Optimal Reinsurance And Investment Problem For Insurers With Loss Aversion

This paper introduces the concept of loss aversion in Behavioral Finance to the reinsurance and investment problem of insurer,and analyses an optimal strategy for a loss-averse insurer.Most investors are risk-averse towards gains,but they will change to be risk-seeking when they suffer from losses,so we assume that the insurer's goal is to chose the optimal strategy to maximize the expected S-shaped utility from the terminal wealth.The surplus process of the insurer is assumed to follow a classical Cram?er-Lundberg model and the insurer is allowed to purchase reinsurance.Moreover,the insurer can invest in a risk-free asset and a risky asset.By martingale approach and lagrange dual theory,we derive the optimal strategy and optimal wealth.We study the optimal strategy under proportional reinsurance and excess-of-loss reinsurance respectively,and numerical examples are provided to illustrate the effects of model parameters on the optimal terminal wealth and the optimal strategy.