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
Publisher
Elsevier BV
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
Funding Information
Financial support from the Society of Actuaries under the CAE research grant.
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
Language
English
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