Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework

Abstract

This paper investigates the asset liability management problem for an ordinary insurance system incorporating the standard concept of proportional reinsurance coverage in a stochastic interest rate and stochastic volatility framework. The goal of the insurer is to maximize the expectation of the constant relative risk aversion (CRRA) of the terminal value of the wealth, while the goal of the reinsurer is to maximize the expected exponential utility (CARA) of the terminal wealth held by the reinsurer. We assume that the financial market consists of risk-free assets and risky assets, and both the insurer and the reinsurer invest on one risk-free asset and one risky asset. By using the stochastic optimal control method, analytical expressions are derived for the optimal reinsurance control strategy and the optimal investment strategies for both the insurer and the reinsurer in terms of the solutions to the underlying Hamilton-Jacobi-Bellman equations and stochastic differential equations for the wealths. Subsequently, a semi-analytical method has been developed to solve the Hamilton-Jacobi-Bellman equation. Finally, we present numerical examples to illustrate the theoretical results obtained in this paper, followed by sensitivity tests to investigate the impact of reinsurance, risk aversion, and the key parameters on the optimal strategies.

Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model

“…Guan et al [32] introduced an inflation index and studied the robust optimal reinsurance and investment problem of fuzzy riskaverse insurance companies, where the stock prices are described using Heston's stochastic volatility model and the interest rates are described via Vasicek's model. Zhang et al [33] introduced stochastic interest rates and stochastic volatility into optimal proportional reinsurance and investment strategies based on insurers' CRRA utility criterion and reinsurers' CARA utility criterion.…”