Time-consistent investment and reinsurance strategies for insurers under multi-period mean-variance formulation with generalized correlated returns

The existing literature on investment and reinsurance is limited to the study of continuous-time problems,while discrete-time problems are always ignored by re-searchers.In this study,we first discuss a multi-period investment and reinsurance opti-mization problem under the classical mean-variance framework.When the asset returns with a serially correlated structure,the time-consistent investment and reinsurance strategies are acquired via backward induction.In addition,we propose an alternative time-consistent mean-variance optimization model that contrasts with the classical mean-variance model,and the corresponding optimal strategy and value function are also derived.We find that the investment and reinsurance strategies are both independent of the current wealth for the above two optimization problems,which coincides with the conclusion presented in the continuous-time problems.Most importantly,the above in-vestment strategies with serially correlated structures are both conditional mean-based strategies,rather than unconditional ones.Finally,we compare the investment and rein-surance strategies suggested above based on the simulation approach,to shed light on which investment-reinsurance strategies are more suitable for insurers.

A Heston local-stochastic volatility model for optimal investment-reinsurance strategy with a defaultable bond in an ambiguous environment

This study considers an optimal investment and reinsurance problem involving a defaultable security for an insurer in an ambiguous environment.In other words,the insurer is ambiguous about the insurance claim that is exponentially distributed with an uncertain rate parameter.The insurer can purchase proportional reinsurance and invest its wealth in three assets:a risk-free asset,a risky asset,the price process of which satisfies the Heston local-stochastic volatility model,and a defaultable corporate bond.For the optimal investment–reinsurance objective with a smooth ambiguity utility proposed by Klibanoff,P.,Marinacci,M.,and Mukerji,S.[A smooth model of decision making under ambiguity,Econometrica,2005,73(6):1849-1892],the equilibrium strategy is introduced and the extended Hamilton–Jacobi–Bellman equation is established through a stochastic control approach.However,the analytical solution of the strategy under the Heston local-stochastic volatility model cannot be obtained because of the complicated nonlinearity of the partial differential equation.In this study,we employ a perturbation method to derive an asymptotic solution for the post-and pre-default cases.In addition,we present a sensitivity analysis to explain the impact of model parameters on the equilibrium investment–reinsurance strategy.