Time-consistent investment-reinsurance strategy with a defaultable security under ambiguous environment

Abstract

<p style='text-indent:20px;'>This paper considers an investment and reinsurance problem with a defaultable security for an insurer in an environment with parameter uncertainties. Suppose that the insurer is ambiguous about the insurance claims. Specifically, the insurance claim is exponentially distributed and the rate parameter is uncertain. The insurer is allowed to invest in a financial market consisting of a risk-free bond, a stock whose price process satisfies the Heston's SV model and a defaultable bond. Moreover, the insurer is allowed to purchase proportional reinsurance and aims to maximize the smooth ambiguity utility proposed in Klibanoff et al. [<xref ref-type="bibr" rid="b15">15</xref>]. By applying stochastic control approach, we establish the extended HJB system and derive the time-consistent investment-reinsurance strategy for the post-default case and the pre-default case, respectively. Finally, a sensitivity analysis is provided to illustrate the effects of model parameters on the equilibrium reinsurance-investment strategy under the smooth ambiguity.</p>