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Article
Optimal consumption and allocation in variable annuities with Guaranteed Minimum Death Benefits
Insurance : Mathematics and Economics
  • Jin GAO, Lingnan University, Hong Kong
  • Eric R. ULM, Georgia State University, Atlanta, USA
Document Type
Journal article
Publication Date
11-1-2012
Keywords
  • GMDB,
  • Variable annuity,
  • Merton model,
  • Expected utility
Abstract

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.

DOI
10.1016/j.insmatheco.2012.08.003
E-ISSN
18735959
Publisher Statement

Copyright © 2012 Elsevier B.V.

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Citation Information
Gao, J., & Ulm, E. R. (2012). Optimal consumption and allocation in variable annuities with Guaranteed Minimum Death Benefits. Insurance: Mathematics and Economics, 51(3), 586-598. doi: 10.1016/j.insmatheco.2012.08.003