Guaranteed Minimum Withdrawal Benefit in Variable Annuities

17 Pages Posted: 22 Feb 2007

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Yue Kuen Kwok

Hong Kong University of Science & Technology - Department of Mathematics

Jianping Zong

National University of Singapore (NUS) - Department of Mathematics

Multiple version iconThere are 2 versions of this paper

Date Written: February 12, 2007

Abstract

We develop a singular stochastic control model for pricing variable annuities with the guaranteed minimum withdrawal benefit. This benefit promises to return the entire initial investment, with withdrawals spread over the term of the contract, irrespective of the market performance of the underlying asset portfolio. A contractual withdrawal rate is set and no penalty is imposed when the policyholder chooses to withdraw at or below this rate. Subject to a penalty fee, the policyholder is allowed to withdraw at a rate higher than the contractual withdrawal rate or surrender the policy instantaneously. We explore the optimal withdrawal strategy adopted by the rational policyholder that maximizes the expected discounted value of the cash flows generated from holding this variable annuity policy. An effcient finite difference algorithm using the penalty approximation approach is proposed for solving the singular stochastic control model. Optimal withdrawal policies of the holders of the variable annuities with the guaranteed minimum withdrawal benefit are explored. We also construct discrete pricing formulation that models withdrawals on discrete dates. Our numerical tests show that the solution values from the discrete model converge to those of the continuous model.

Keywords: guaranteed minimum withdrawal benefit, variable annuities, singular stochastic control model

JEL Classification: G13

Suggested Citation

Dai, Min and Kwok, Yue Kuen and Zong, Jianping, Guaranteed Minimum Withdrawal Benefit in Variable Annuities (February 12, 2007). Available at SSRN: https://ssrn.com/abstract=964083 or http://dx.doi.org/10.2139/ssrn.964083

Min Dai

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Yue Kuen Kwok (Contact Author)

Hong Kong University of Science & Technology - Department of Mathematics ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong

Jianping Zong

National University of Singapore (NUS) - Department of Mathematics ( email )

Department of Mathematics
Singapore, 117543
Singapore

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