Efficient valuation of joint life variable annuities with guaranteed minimum death benefits

Jiayi Xie; Zhimin Zhang; Zhenyu Cui

doi:10.1016/j.matcom.2025.04.001

Efficient valuation of joint life variable annuities with guaranteed minimum death benefits

Jiayi Xie, Zhimin Zhang, Zhenyu Cui

School of Business

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we introduce an efficient valuation method for variable annuities (VAs) with guaranteed minimum death benefits (GMDBs), where the benefits depend on the combined survival status of two lives, such as for a married couple. We assume a general exponential Lévy process for the risky asset price and propose an innovative combination of bivariate Laguerre series expansions with the projection (PROJ) method for valuing joint life VAs. We derive explicit approximation formulas for three types of GMDB riders. Numerical examples demonstrate that the proposed method is both highly accurate and computationally efficient.

Original language	English
Pages (from-to)	135-153
Number of pages	19
Journal	Mathematics and Computers in Simulation
Volume	236
DOIs	https://doi.org/10.1016/j.matcom.2025.04.001
State	Published - Oct 2025

Keywords

Joint life status
Laguerre series
Projection method
Variable annuities

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10.1016/j.matcom.2025.04.001

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title = "Efficient valuation of joint life variable annuities with guaranteed minimum death benefits",

abstract = "In this paper, we introduce an efficient valuation method for variable annuities (VAs) with guaranteed minimum death benefits (GMDBs), where the benefits depend on the combined survival status of two lives, such as for a married couple. We assume a general exponential L{\'e}vy process for the risky asset price and propose an innovative combination of bivariate Laguerre series expansions with the projection (PROJ) method for valuing joint life VAs. We derive explicit approximation formulas for three types of GMDB riders. Numerical examples demonstrate that the proposed method is both highly accurate and computationally efficient.",

keywords = "Joint life status, Laguerre series, Projection method, Variable annuities",

author = "Jiayi Xie and Zhimin Zhang and Zhenyu Cui",

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T1 - Efficient valuation of joint life variable annuities with guaranteed minimum death benefits

AU - Xie, Jiayi

AU - Zhang, Zhimin

AU - Cui, Zhenyu

PY - 2025/10

Y1 - 2025/10

N2 - In this paper, we introduce an efficient valuation method for variable annuities (VAs) with guaranteed minimum death benefits (GMDBs), where the benefits depend on the combined survival status of two lives, such as for a married couple. We assume a general exponential Lévy process for the risky asset price and propose an innovative combination of bivariate Laguerre series expansions with the projection (PROJ) method for valuing joint life VAs. We derive explicit approximation formulas for three types of GMDB riders. Numerical examples demonstrate that the proposed method is both highly accurate and computationally efficient.

AB - In this paper, we introduce an efficient valuation method for variable annuities (VAs) with guaranteed minimum death benefits (GMDBs), where the benefits depend on the combined survival status of two lives, such as for a married couple. We assume a general exponential Lévy process for the risky asset price and propose an innovative combination of bivariate Laguerre series expansions with the projection (PROJ) method for valuing joint life VAs. We derive explicit approximation formulas for three types of GMDB riders. Numerical examples demonstrate that the proposed method is both highly accurate and computationally efficient.

KW - Joint life status

KW - Laguerre series

KW - Projection method

KW - Variable annuities

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M3 - Article

AN - SCOPUS:105002562010

SN - 0378-4754

VL - 236

SP - 135

EP - 153

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

ER -

Efficient valuation of joint life variable annuities with guaranteed minimum death benefits

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Keywords

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