Time-consistent proportional reinsurance and investment strategies under ambiguous environment

In this paper, we study the equilibrium proportional reinsurance and investment strategies for an insurer in an environment with parameter uncertainties. The insurer can buy proportional reinsurance business to hedge its insurance risks. However, the insurer is ambiguous about the insurance claims and risky assets. Specifically, the insurance claim is exponentially distributed and the rate parameter is uncertain. Besides, the return of a stock is uncertain. The insurer holds ambiguous beliefs over these states. The goal of the insurer is to maximize the smooth ambiguity utility proposed in Klibanoff et al. (2005). The equilibrium control is introduced to derive the time-consistent solution. In the end, a sensitivity analysis is presented to show the economic behaviors of the insurer under the smooth ambiguity. Results reveal that the uncertain beliefs play an important role in the equilibrium reinsurance and investment strategies. When the insurer is more risk averse towards ambiguity, the insurer will invest less in the ambiguous asset and more in the non-ambiguous asset. (C) 2018 Elsevier B.V. All rights reserved.