简短交流：当保费由凸函数计算时，实现指数效用最大化的最优保险

IF 1.4 4区经济学 Q3 BUSINESS, FINANCE

SIAM Journal on Financial Mathematics Pub Date : 2024-03-08 DOI:10.1137/23m1601237

Jingyi Cao, Dongchen Li, Virginia R. Young, Bin Zou

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引用次数: 0

摘要

SIAM 金融数学期刊》，第 15 卷第 1 期，第 SC15-SC27 页，2024 年 3 月。摘要。我们找到了最优赔偿金，以最大化保险购买者终端财富的期望效用，其偏好是以指数效用为模型的。保险费由一个凸函数计算。我们得到了最优赔偿金的必要条件；然后，由于候选最优赔偿金是隐含给出的，我们利用该必要条件开发了一种数值算法来计算它。我们证明，数值算法会收敛到一个唯一的补偿，而这个补偿确实等于最优政策。我们还将用实例来说明我们的结果。

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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Short Communication: Optimal Insurance to Maximize Exponential Utility When Premium Is Computed by a Convex Functional

SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page SC15-SC27, March 2024.
Abstract. We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex functional. We obtain a necessary condition for the optimal indemnity; then, because the candidate optimal indemnity is given implicitly, we use that necessary condition to develop a numerical algorithm to compute it. We prove that the numerical algorithm converges to a unique indemnity that, indeed, equals the optimal policy. We also illustrate our results with numerical examples.

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来源期刊

SIAM Journal on Financial Mathematics MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： SIAM Journal on Financial Mathematics (SIFIN) addresses theoretical developments in financial mathematics as well as breakthroughs in the computational challenges they encompass. The journal provides a common platform for scholars interested in the mathematical theory of finance as well as practitioners interested in rigorous treatments of the scientific computational issues related to implementation. On the theoretical side, the journal publishes articles with demonstrable mathematical developments motivated by models of modern finance. On the computational side, it publishes articles introducing new methods and algorithms representing significant (as opposed to incremental) improvements on the existing state of affairs of modern numerical implementations of applied financial mathematics.