Optimal Ratio Reinsurance and Investment Strategy under VaR Constraint
This paper investigates the optimal investment and reinsurance strategy selection problem for an insurer under VaR dynamic constraints.Suppose that the insurer chooses proportional reinsurance to spread the claims risk and increase the extra return by means of bank deposit and stock investment,where the stock price satisfies the Heston model.The goal of the insurer is to seek the optimal strategy that maximizes the expected utility of its terminal wealth.By introducing the VaR constraint condition and using the expected Utility maximization criterion,the stochastic control problem with VaR constraint is established,and then the HJB equation is derived by using the stochastic control theory.Furthermore,by using Lagrange functions and other methods,the optimal strategies under exponential utility are obtained when the VAR constraints are active and inactive for the insurer.In addition,the optimal investment strategy for the only investment case is considered.Finally,the sensitivity of the optimal strategy is analyzed by simulation.
VaR constraintHeston modelLagrange functionoptimal reinsurance and investment strategy
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