Journal of Mathematics and Modeling in Finance

Valuation of Variable Annuities with Guaranteed Minimum Withdrawal Benefits under Continuous Withdrawal Strategies

Articles in Press

Document Type : Research Article

Authors

Ali Safdari Vaighani 1
Azadeh Salehi 2

1 Department of Mathematics‎, ‎Allameh Tabataba'i University‎, ‎Tehran‎, ‎Iran.

2 ECO College of Insurance, Allameh Tabataba'i University, Tehran, Iran.

10.22054/jmmf.2026.91363.1260
Abstract
The life insurance industry has experienced substantial growth in recent years, accompanied by the development of a wide range of insurance and retirement products. Among these products, variable annuities (VAs) with Guaranteed Minimum Withdrawal Benefits (GMWBs) have attracted considerable attention because they combine the investment features of variable annuities with guarantees that protect policyholders against adverse market performance. In particular, a GMWB rider allows the policyholder to withdraw a predetermined amount periodically while providing a guarantee designed to recover the initial investment, subject to the contractual conditions. In this paper, we study the mathematical modeling and valuation of variable annuities with GMWB riders. A pricing framework for the associated guarantee is formulated, and numerical approximations are obtained using finite difference methods. Furthermore, the effects of various model and contract parameters on the value of the GMWB rider are investigated through numerical experiments.

Keywords

Variable Annuities
Guaranteed Minimum Withdrawal Benefit (GMWB)
Life Insurance
Insurance Fees, Finite Difference Method
[1] W. H. Fleming, and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer, (2006) 2nd ed., New York.
[2] V. Horneff, R. Maurer, O. S. Mitchell, and M. Z. Stamos, Variable Annuities with Guaranteed Minimum Lifetime Withdrawal Benefits, Insurance: Mathematics and Economics, (2015) vol. 64 pp. 246–258.
[3] A. R. Bacinello, P. Millossovich, A. Olivieri, and E. Pitacco, Variable Annuities: A Unifying Valuation Approach, Insurance: Mathematics and Economics, (2011) vol. 48 no. 3 pp. 393–410.
[4] M. A. Milevsky, and S. E. Posner, The titanic option: valuation of the guaranteed minimum death benefit in variable annuities and mutual funds, Journal of Risk and Insurance, (2001) pp. 93–128.
[5] M. A. Milevsky, and T. S. Salisbury, Financial valuation of guaranteed minimum withdrawal benefits, Insurance: Mathematics and Economics, (2006) vol. 38 no. 1 pp. 21–38.
[6] M. Dai, Y. K. Kwok, and J. Zong, Guaranteed minimum withdrawal benefit in variable annuities, Mathematical Finance, (2008) vol. 18 no. 4 pp. 595–611.
[7] T. F. Coleman, Y. Li, and M.-C. Patron, Hedging guarantees in variable annuities under both equity and interest rate risks, Insurance: Mathematics and Economics, (2006) vol. 38 no. 2 pp. 215–228.
Journal of Mathematics and Modeling in Finance

Articles in Press, Accepted Manuscript
Available Online from 17 October 2026

  • Receive Date 06 February 2026
  • Revise Date 17 July 2026
  • Accept Date 28 August 2026

Home

Editorial Board

Guide for Authors

Submit Manuscript

Contact Us