Bulletin of the
Korean Mathematical Society BKMS

This paper studies the optimal surrender policies for a variable annuity (VA) contract with a surrender option and a fixed insurance fee for guaranteed minimum maturity benefits (GMMB). In our proposed model, a policyholder pays the fixed insurance fee. Based on the integral transform techniques, we derive the analytic integral equations for the optimal surrender boundary and the value function of the VA contract that can be solved numerically by recursive integration method. We provide numerical values for the value function, the optimal surrender boundary, and the expected optimal surrender time.

Keywords: Variable annuity, surrender option, guaranteed minimum maturity benefits, fixed insurance fee, integral equation

MSC numbers: Primary 37H10, 35Q93, 91-08

Supported by: Junkee Jeon received support from the Young Research Program of the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT \& Future Planning (NRF-2020R1C1C1A01007313). Kyunghyun Park received support from the NRF Global Ph.D Fellowship (2016H1A2A1908911)