On the Maximum Principle for Optimal Control Problems of Stochastic Volterra Integral Equations with Delay

Hamaguchi, Yushi

doi:10.1007/s00245-022-09958-w

Cited by 5 publications

(1 citation statement)

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“…Stochastic differential equations have various applications in various fields, such as medicine, economics, and social sciences, as well as engineering, biology, and financial mathematics. These equations play a crucial role in modelling population growth, where the stochastic Volterra-Fredholm integral equation is fundamental; see [1][2][3][4][5][6][7]. A stochastic Volterra-Fredholm integral equations can be modeled using several types of stochastic differential equations or, in more complicated cases, nonlinear stochastic differential equations of the Itô type [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution for stochastic Volterra-Fredholm integral equations with delay arguments

Yao,

Zhang,

Shi

2024

Acta Polytech

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We present a method for computing the stochastic operational matrix of integration to advance the study of stochastic Volterra-Fredholm integral equations (SVFIEs) based on delay arguments. First, the method evaluates the combined effects of the delay and its parameters on the accuracy improvement of the convergence rate. Our results can be applied to SVFIEs, with the operational delay matrices of the block pulse function simplified to algebraic ones. Numerical calculations were performed on a PC using Python 3 programs. Results also demonstrate the accuracy of approximate solutions; arithmetic operations are carried out without the need for derivation or integration.

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Section: Introductionmentioning

confidence: 99%

Numerical solution for stochastic Volterra-Fredholm integral equations with delay arguments

Yao,

Zhang,

Shi

2024

Acta Polytech

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Pontryagin Maximum Principle for Fractional Delay Differential Equations and Controlled Weakly Singular Volterra Delay Integral Equations

Gasimov,

Asadzade,

Mahmudov

2024

Qual. Theory Dyn. Syst.

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This article explores two distinct issues. To begin with, we analyze the Pontriagin maximum principle concerning fractional delay differential equations. Furthermore, we investigate the most effective method for resolving the control problem associated with Eq. (1.1) and its corresponding payoff function (1.2). Subsequently, we explore the Pontryagin Maximum principle within the framework of Volterra delay integral equations (1.3). We enhance the outcomes of our investigation by presenting illustrative examples towards the conclusion of the article.

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Linear-quadratic stochastic volterra controls II. Optimal strategies and Riccati-Volterra equations

Hamaguchi,

Wang

2024

ESAIM: COCV

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In this paper, we study linear-quadratic control problems for stochastic Volterra integral equations with singular and non-convolution-type coefficients. The weighting matrices in the cost functional are not assumed to be non-negative definite. From a new viewpoint, we formulate a framework of causal feedback strategies. The existence and the uniqueness of a causal feedback optimal strategy are characterized by means of the corresponding Riccati--Volterra equation. The causal feedback optimal strategy is explicitly written by a finite dimensional (matrix-valued) function which solves the Riccati--Volterra equation.

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On the Maximum Principle for Optimal Control Problems of Stochastic Volterra Integral Equations with Delay

Cited by 5 publications

References 20 publications

Numerical solution for stochastic Volterra-Fredholm integral equations with delay arguments

Numerical solution for stochastic Volterra-Fredholm integral equations with delay arguments

Pontryagin Maximum Principle for Fractional Delay Differential Equations and Controlled Weakly Singular Volterra Delay Integral Equations

Linear-quadratic stochastic volterra controls II. Optimal strategies and Riccati-Volterra equations

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