Optimization of Dynamic Guaranteed Minimum Return, Investment And Reinsurance Strategy By Balancing the Risks And Benefit of Both Insurers And Consumers
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In this article, we model and discuss determination of optimal minimum guaranteed rate of return, as well as optimal investment and reinsurance strategies of universal life insurance by minimizing both the investment risk and the risk of obtaining guaranteed return, with the constraint of surplus larger than a prescribed constant. We also discuss the application of dynamic programming in finding dynamic solutions to these optimization problems. We analyse the affect of the change of the risk-free interest rate, the age of insured, the cost of reinsurance, and mortality on optimal solutions. Our results indicate that changes in the insured age, in the risk-free interest rate (when risk-free interest rate takes high value), and of mortality will not materially affect the optimal value of minimum guaranteed return rate, investment and reinsurance strategies except for the situation when mortality decreases. However, changing these parameters will affect the sum of the volatilities of investment and minimum guaranteed return rate and the surplus of the insurer. The results also indicate that the optimal and sub-optimal minimum guarantee return rates are very low when risk-free interest rate is very low ().
Abstract
In this article, we model and discuss determination of optimal minimum guaranteed rate of return, as well as optimal investment and reinsurance strategies of universal life insurance by minimizing both the investment risk and the risk of obtaining guaranteed return, with the constraint of surplus larger than a prescribed constant. We also discuss the application of dynamic programming in finding dynamic solutions to these optimization problems. We analyse the affect of the change of the risk-free interest rate, the age of insured, the cost of reinsurance, and mortality on optimal solutions. Our results indicate that changes in the insured age, in the risk-free interest rate (when risk-free interest rate takes high value), and of mortality will not materially affect the optimal value of minimum guaranteed return rate, investment and reinsurance strategies except for the situation when mortality decreases. However, changing these parameters will affect the sum of the volatilities of investment and minimum guaranteed return rate and the surplus of the insurer. The results also indicate that the optimal and sub-optimal minimum guarantee return rates are very low when risk-free interest rate is very low ().
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