Title

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

Document Type

Journal article

Source Publication

Insurance : Mathematics and Economics

Publication Date

11-1-2012

Volume

51

Issue

3

First Page

586

Last Page

598

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

Print ISSN

01676687

E-ISSN

18735959

Publisher Statement

Copyright © 2012 Elsevier B.V.

Access to external full text or publisher's version may require subscription.

Full-text Version

Publisher’s Version

Recommended Citation

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