Abstract
This paper considers the reinsurance-investment problem with interest rate risks under constant relative risk aversion and constant absolute risk aversion preferences, respectively. Stochastic control theory and dynamic programming principle are applied to investigate the optimal proportional reinsurance-investment strategy for an insurer under the Vasicek stochastic interest rate model. Solving the corresponding Hamilton-Jacobi-Bellman equation via the Legendre transform approach, the optimal premium allocation strategies maximizing the expected utilities of terminal wealth are derived. In addition, several sensitivity analyses and numerical illustrations are given to analyze the impacts of different risk preferences and interest rate fluctuation on the optimal strategies. We find that the asset allocation and reinsurance ratio of the insurer are correlated with risk preference coefficient and interest rate fluctuation, and the insurance company may adjust the reinsurance-investment strategy to deal with interest rate risk.
Highlights
As a financial institution, insurance company plays an important role in the modern society, and its reinsurance and investment business is the focus of the management because reinsurance and investment are effective at dispersing risks and making profits from surplus
The first contribution of this paper is that we consider the stochastic interest rate in the reinsurance-investment problem, and the stochastic interest rate model and surplus process are different from Guan and Liang [20]
Since the insurer is allowed to buy reinsurance and invest in the financial market, the trading strategy is a pair of dynamic process which is denoted by Π: (q(t), π(t)), where q(t) represents the reinsurance strategy and π(t) denotes the investment strategy
Summary
Insurance company plays an important role in the modern society, and its reinsurance and investment business is the focus of the management because reinsurance and investment are effective at dispersing risks and making profits from surplus. Browne [1] obtained the optimal investment strategy under the diffusion model through the Hamilton–Jacobi–Bellman (HJB) equation, creating a precedent of combining risk theory with stochastic control theory. For the reinsurance-investment problem, Liang et al [19] used an Ornstein-Uhlenbeck process to describe the Discrete Dynamics in Nature and Society instantaneous rate of investment return under CRRA utility maximization, and inflation risks are further considered in Guan and Liang [20]. The first contribution of this paper is that we consider the stochastic interest rate in the reinsurance-investment problem, and the stochastic interest rate model and surplus process are different from Guan and Liang [20]. Erefore, on the basis of the stochastic control theory, we use Legendre transformation to obtain the explicit expression of the optimal strategy.
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