• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.349-364
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• 2021

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.