随机延迟微分方程的最优控制及其在路径依赖金融和经济模型中的应用

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-05-20 DOI:10.1137/23m1553960

Filippo De Feo, Salvatore Federico, Andrzej Święch

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 3 期第 1490-1520 页，2024 年 6 月。摘要在本手稿中，我们考虑了一类随机微分延迟方程的最优控制问题。首先，我们在合适的无穷维希尔伯特空间中重写问题。然后，利用动态编程方法，我们将问题的值函数表征为相关无穷维汉密尔顿-雅各比-贝尔曼方程的唯一粘性解。最后，我们证明了值函数的[数学]部分正则性。我们将这些结果应用于路径依赖的金融和经济问题（类似默顿的投资组合问题和最优广告）。

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Optimal Control of Stochastic Delay Differential Equations and Applications to Path-Dependent Financial and Economic Models

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1490-1520, June 2024.
Abstract. In this manuscript we consider a class of optimal control problems of stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we characterize the value function of the problem as the unique viscosity solution of the associated infinite-dimensional Hamilton-Jacobi-Bellman equation. Finally, we prove a [math]-partial regularity of the value function. We apply these results to path dependent financial and economic problems (Merton-like portfolio problem and optimal advertising).

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.