An analytical study of participating policies with minimum rate guarantee and surrender option. (English) Zbl 1484.91379
Summary: 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 E. Ekström and J. Vaicenavicius [Stochastic Processes Appl. 130, No. 2, 806–823 (2020; Zbl 1441.60034)]. Financial implications of this strategy are discussed in detail and supported by extensive numerical experiments.
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 E. Ekström and J. Vaicenavicius [Stochastic Processes Appl. 130, No. 2, 806–823 (2020; Zbl 1441.60034)]. Financial implications of this strategy are discussed in detail and supported by extensive numerical experiments.
MSC:
| 91G05 | Actuarial mathematics |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
| 35R35 | Free boundary problems for PDEs |
Keywords:
participating policies; minimum rate guarantee; surrender option; solvency requirement; optimal stopping; free-boundary problems; stop-loss boundary; too-good-to-persist boundaryCitations:
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