{"title":"Efficient valuation of joint life variable annuities with guaranteed minimum death benefits","authors":"Jiayi Xie , Zhimin Zhang , Zhenyu Cui","doi":"10.1016/j.matcom.2025.04.001","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"236 ","pages":"Pages 135-153"},"PeriodicalIF":4.4000,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Computers in Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S037847542500120X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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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.
期刊介绍：
The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles.
Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO.
Topics covered by the journal include mathematical tools in:
•The foundations of systems modelling
•Numerical analysis and the development of algorithms for simulation
They also include considerations about computer hardware for simulation and about special software and compilers.
The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research.
The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.
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