Optimal consumption and allocation in variable annuities with Guaranteed Minimum Death Benefits

Jin GAO, Eric R. ULM

Research output: Journal PublicationsJournal Article (refereed)peer-review

23 Citations (Scopus)


We determine the optimal allocation of funds between the fixed and variable subaccounts in a variable annuity with a GMDB (Guaranteed Minimum Death Benefit) clause featuring partial withdrawals by using a utility-based approach. The Merton method is applied by assuming that individuals allocate funds optimally in order to maximize the expected utility of lifetime consumption. It also reflects bequest motives by including the recipient’s utility in terms of the policyholder’s guaranteed death benefits. We derive the optimal transfer choice by the insured, and furthermore price the GMDB through maximizing the discounted expected utility of the policyholders and beneficiaries by investing dynamically in the fixed account and variable fund and withdrawing optimally.
Original languageEnglish
Pages (from-to)586-598
Number of pages13
JournalInsurance : Mathematics and Economics
Issue number3
Publication statusPublished - 1 Nov 2012


  • Expected utility
  • GMDB
  • Merton model
  • Variable annuity

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