分数布朗运动的随机控制

IF 0.3 Q4 STATISTICS & PROBABILITY

Random Operators and Stochastic Equations Pub Date : 2024-02-01 DOI:10.1515/rose-2023-2025

Ikram Hamed, A. Chala

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引用次数: 0

摘要

我们考虑了一个由分数布朗运动驱动的非线性前向后向随机微分方程的随机控制问题，该微分方程的赫斯特参数 H∈ ( 0 , 1 ) {H\in(0,1)}，在控制域集合为凸的情况下。我们提供了解的估计，并以随机最大原则的形式建立了必要和充分的最优条件。

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Stochastic controls of fractional Brownian motion

We consider a stochastic control problem for a non-linear forward-backward stochastic differential equation driven by fractional Brownian motion, with Hurst parameter H ∈ ( 0 , 1 ) {H\in(0,1)} , in the case where the set of the control domain is convex. We provide an estimation of the solution and establish the necessary and sufficient optimality conditions in the form of the stochastic maximum principle. We apply the theory to solve a linear quadratic stochastic control problem.

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来源期刊

Random Operators and Stochastic Equations STATISTICS & PROBABILITY-

CiteScore

0.60

自引率

25.00%

发文量