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An analytical study of participating policies with minimum guaranteed and surrender option

Maria B. Chiarolla, Tiziano De Angelis and Gabriele Stabile

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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 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 peculiar structure of the optimal surrender strategy, which was undetected by previous (mostly numerical) studies on the same topic. For that we develop new methods in order to study the regularity of the corresponding optimal stopping boundaries.

Date: 2020-04
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Handle: RePEc:arx:papers:2004.06982