An analytical study of participating policies with minimum rate guarantee and surrender option
对一类具有最低利率保证和退保选择权的参与型保单进行理论分析，发现最优退保策略由两个止损边界和一个“好到不能持续”边界触发，并通过数值实验验证其金融含义。
Abstract We perform a detailed theoretical study of the value of a class of participating policies with four key features: (i) the policyholder is guaranteed a minimum interest rate on the policy reserve; (ii) the contract can be terminated by the holder at any time until maturity (surrender option); (iii) at the maturity (or upon surrender), a bonus is credited to the holder if the portfolio backing the policy outperforms the current policy reserve; (iv) due to solvency requirements, the contract ends if the value of the underlying portfolio of assets falls below the policy reserve. Our analysis is probabilistic and relies on optimal stopping and free boundary theory. We find a structure of the optimal surrender strategy which was undetected by previous (mostly numerical) studies on the topic. Optimal surrender of the contract is triggered by two ‘stop-loss’ boundaries and by a ‘too-good-to-persist’ boundary (in the language of Ekström and Vaicenavicius in Stoch. Process. Appl. 130: 806–823, 2020). Financial implications of this strategy are discussed in detail and supported by extensive numerical experiments.