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

Jin GAO, Eric R. ULM

Research output: Journal PublicationsJournal Article (refereed)

13 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)586-598
Number of pages13
JournalInsurance : Mathematics and Economics
Volume51
Issue number3
DOIs
Publication statusPublished - 1 Nov 2012

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Expected Utility
Optimal Allocation
Lifetime
Maximise
Partial
Optimal allocation
Optimal consumption
Variable annuities
Expected utility
Investing
Bequest motive

Keywords

  • Expected utility
  • GMDB
  • Merton model
  • Variable annuity

Cite this

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Optimal consumption and allocation in variable annuities with Guaranteed Minimum Death Benefits. / GAO, Jin; ULM, Eric R.

In: Insurance : Mathematics and Economics, Vol. 51, No. 3, 01.11.2012, p. 586-598.

Research output: Journal PublicationsJournal Article (refereed)

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AU - ULM, Eric R.

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AB - 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.

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KW - GMDB

KW - Merton model

KW - Variable annuity

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