跳跃扩散模型中效用最大化的前向后向 SDEs 系统

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-04-20 DOI:10.1007/s00245-024-10114-9

Marina Santacroce, Paola Siri, Barbara Trivellato

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引用次数: 0

摘要

我们考虑的经典问题是，在一个简单的跳跃-扩散模型中，最大化最终净财富的预期效用与最终随机负债。本着 Horst 等人（Stoch Process Appl 124(5):1813-1848, 2014）和 Santacroce 和 Trivellato（SIAM J Control Optim 52(6):3517-3537, 2014）的精神，在合适的条件下，最优策略以隐式形式表达为前向后向方程组。本文给出了纯跳跃模型和指数效用的一些显式结果。

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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Forward Backward SDEs Systems for Utility Maximization in Jump Diffusion Models

We consider the classical problem of maximizing the expected utility of terminal net wealth with a final random liability in a simple jump-diffusion model. In the spirit of Horst et al. (Stoch Process Appl 124(5):1813–1848, 2014) and Santacroce and Trivellato (SIAM J Control Optim 52(6):3517–3537, 2014), under suitable conditions the optimal strategy is expressed in implicit form in terms of a forward backward system of equations. Some explicit results are presented for the pure jump model and for exponential utilities.

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.