An optimal control problem for a Wiener process with random infinitesimal mean

IF 0.6 Q3 MULTIDISCIPLINARY SCIENCES

Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali Pub Date : 2019-12-20 DOI:10.1478/AAPP.97S2A1

M. Lefebvre, Abderrazak Moutassim

引用次数: 2

Abstract

We consider a stochastic optimal control problem for one-dimensional diffusion processes with random infinitesimal mean and variance that depend on a continuoustime Markov chain. The process is controlled until it reaches either end of an interval. The aim is to minimize the expected value of a cost criterion with quadratic control costs on the way and a final cost. A particular case with a Wiener process will be treated in detail. Approximate and numerical solutions will be presented.

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具有随机无穷小均值的Wiener过程的最优控制问题

研究了一类具有随机无限小均值和方差的一维扩散过程的随机最优控制问题，该扩散过程依赖于连续时间马尔可夫链。过程被控制，直到它到达间隔的任意一端。其目的是使成本准则的期望值最小化，并使途中的二次控制成本和最终成本最小化。我们将详细讨论维纳过程的特殊情况。将给出近似解和数值解。

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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来源期刊

Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali MULTIDISCIPLINARY SCIENCES-

CiteScore

3.80

自引率

0.00%

发文量

审稿时长

31 weeks

期刊介绍： This journal is of a multi- and inter-disciplinary nature and covers a broad range of fields including mathematics, computer science, physics, chemistry, biology, earth sciences, and their intersection. History of science is also included within the topics addressed by the journal. The transactions of the Pelorian Academy started out as periodic news sheets containing the notes presented by the members of the Divisions into which the Academy has been and still is organized, according to subject areas. The publication of these notes for the Division (“Classe”) of Mathematical, Physical and Natural Sciences is the responsibility of the Editorial Committee, which is composed of the Director of the division with the role of Chairman, the Vice-Director, the Secretary and two or more other members. Besides original research articles, the journal also accepts texts from conferences and invited talks held in the Academy. These contributions are published in a different section of the journal. In addition to the regular issues, single monographic supplements are occasionally published which assemble reports and communications presented at congresses, symposia, seminars, study meetings and other scientific events organized by the Academy or under its patronage. Since 2004 these transactions have been published online in the form of an open access electronic journal.