通过粘性解法解决状态和控制中存在延迟的随机最优控制问题，并将其应用于最优广告和最优投资问题

IF 1.4 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS

Decisions in Economics and Finance Pub Date : 2024-06-07 DOI:10.1007/s10203-024-00456-y

Filippo de Feo

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引用次数: 0

摘要

在本手稿中，我们考虑的是状态和控制均有延迟的随机微分方程的最优控制问题。首先，我们证明了状态方程在希尔伯特空间上的等效马尔可夫重述。然后，利用无穷维系统的动态编程方法，我们证明了值函数是无穷维汉密尔顿-雅各比-贝尔曼方程的唯一粘性解。我们将这些结果应用于经济学问题：随机最优广告问题和有建设时间的随机最优投资问题。

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Stochastic optimal control problems with delays in the state and in the control via viscosity solutions and applications to optimal advertising and optimal investment problems

In this manuscript we consider optimal control problems of stochastic differential equations with delays in the state and in the control. First, we prove an equivalent Markovian reformulation on Hilbert spaces of the state equation. Then, using the dynamic programming approach for infinite-dimensional systems, we prove that the value function is the unique viscosity solution of the infinite-dimensional Hamilton-Jacobi-Bellman equation. We apply these results to problems coming from economics: stochastic optimal advertising problems and stochastic optimal investment problems with time-to-build.

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来源期刊

Decisions in Economics and Finance SOCIAL SCIENCES, MATHEMATICAL METHODS-

CiteScore

2.50

自引率

9.10%

发文量

期刊介绍： Decisions in Economics and Finance: A Journal of Applied Mathematics is the official publication of the Association for Mathematics Applied to Social and Economic Sciences (AMASES). It provides a specialised forum for the publication of research in all areas of mathematics as applied to economics, finance, insurance, management and social sciences. Primary emphasis is placed on original research concerning topics in mathematics or computational techniques which are explicitly motivated by or contribute to the analysis of economic or financial problems.