Analytic valuation of GMDB options with utility based asset allocation

IF 1.6 3区经济学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Scandinavian Actuarial Journal Pub Date : 2022-03-09 DOI:10.1080/03461238.2022.2034127

Eric R. Ulm

引用次数: 1

Abstract

A number of analytic solutions have been found for Variable Annuity Guaranteed Minimum Death Benefit (GMDB) option values under a variety of mortality laws. To date, the solutions are for Risk-Neutral valuation only. Where policyholder decisions are allowed, it is assumed that they act to maximize the risk-neutral value of the GMDB. We examine situations where the asset allocation decisions are made to maximize expected utility rather than option value. We find analytic solutions for both return of premium and ratchet options at small values of bequest motive for a number of mortality laws.

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基于效用的资产配置GMDB期权分析估值

在各种死亡规律下，对可变年金保证最低死亡收益(GMDB)期权值进行了分析。迄今为止，这些解决方案仅适用于风险中性估值。在允许保单持有人决策的情况下，假设他们的行为是为了最大化GMDB的风险中性价值。我们研究了资产配置决策是为了最大化预期效用而不是期权价值的情况。我们找到了在遗赠动机的小值条件下保费回报和棘轮期权的解析解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Scandinavian Actuarial Journal MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-STATISTICS & PROBABILITY

CiteScore

3.30

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Scandinavian Actuarial Journal is a journal for actuarial sciences that deals, in theory and application, with mathematical methods for insurance and related matters. The bounds of actuarial mathematics are determined by the area of application rather than by uniformity of methods and techniques. Therefore, a paper of interest to Scandinavian Actuarial Journal may have its theoretical basis in probability theory, statistics, operations research, numerical analysis, computer science, demography, mathematical economics, or any other area of applied mathematics; the main criterion is that the paper should be of specific relevance to actuarial applications.