指数莱维转换模型的效用最大化

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Theory of Probability and its Applications Pub Date : 2024-05-02 DOI:10.1137/s0040585x97t991799

Y. Dong, L. Vostrikova

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引用次数: 0

摘要

概率论及其应用》（Theory of Probability &Its Applications），第 69 卷第 1 期，第 127-149 页，2024 年 5 月。本文致力于通过对偶法最大化有限时间间隔上指数莱维切换过程的 HARA（双曲绝对风险厌恶）效用。文中给出了涉及海灵格和库尔贝克--莱布勒过程的所有$f$-发散最小马廷式度量的描述及其拉顿-尼科戴姆密度的表达式。推导了在逐步扩大的过滤中实现 HARA 效用最大化的最优策略以及相应的最大期望效用值。以布朗转换模型为例，通过价值过程对结果进行了金融解释。

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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Utility Maximization of the Exponential Lévy Switching Models

Theory of Probability &Its Applications, Volume 69, Issue 1, Page 127-149, May 2024.
This article is devoted to maximization of HARA (hyperbolic absolute risk aversion) utilities of the exponential Lévy switching processes on a finite time interval via the dual method. The description of all $f$-divergence minimal martingale measures and the expression of their Radon--Nikodým densities involving the Hellinger and Kulback--Leibler processes are given. The optimal strategies in progressively enlarged filtration for the maximization of HARA utilities as well as the values of the corresponding maximal expected utilities are derived. As an example, the Brownian switching model is presented with financial interpretations of the results via the value process.

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来源期刊

Theory of Probability and its Applications 数学-统计学与概率论

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

6 months

期刊介绍： Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.