具有最低费率保证和退保选择权的分红保单的分析研究
An analytical study of participating policies with minimum rate guarantee and surrender option
摘要：
我们对一类参与保单的价值进行了详细的理论研究，该保单具有四个关键特征：$(i)$，保单持有人获得保单准备金最低利率保证; $(ii)$，持有人可以随时终止合同，直至到期（退保选择权）;到期时的$(iii)$（或在退保时）如果支持保单的投资组合表现优于当前保单储备，则可向持有人发放奖金; $(iv)$由于偿付能力要求，如果基础资产组合的价值低于保单准备金，则合同终止。我们的分析是概率的，它依赖于最优停时和自由边界理论。我们发现了一个结构的最佳投降策略，这是未被发现的以前（主要是数值）的研究相同的主题。合约的最佳放弃是由两个“止损”边界和一个“太好而不能持续”边界（用\cite{EV20}的语言）触发的。这一战略的财政影响进行了详细讨论，并支持广泛的数值实验。
英文摘要：
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 can be 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 it 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 same 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 \cite{EV20}). Financial implications of this strategy are discussed in detail and supported by extensive numerical experiments.
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