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Pontryagin’s Risk-Sensitive Stochastic Maximum Principle for Backward Stochastic Differential Equations with Application

Pontryagin’s Risk-Sensitive Stochastic Maximum Principle for Backward Stochastic Differential... This paper studies the risk-sensitive optimal control problem for a backward stochastic system. More precisely, we set up a necessary stochastic maximum principle for a risk-sensitive optimal control of this kind of equations. The control domain is assumed to be convex and the generator coefficient of such system is allowed to be depend on the control variable. As a preliminary step, we study the risk-neutral problem for which an optimal solution exists. This is an extension of initial control system to this type of problem, where the set of admissible controls is convex. An example to carried out to illustrate our main result of risk-sensitive control problem under linear stochastic dynamics with exponential quadratic cost function. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

Pontryagin’s Risk-Sensitive Stochastic Maximum Principle for Backward Stochastic Differential Equations with Application

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References (9)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-017-0031-2
Publisher site
See Article on Publisher Site

Abstract

This paper studies the risk-sensitive optimal control problem for a backward stochastic system. More precisely, we set up a necessary stochastic maximum principle for a risk-sensitive optimal control of this kind of equations. The control domain is assumed to be convex and the generator coefficient of such system is allowed to be depend on the control variable. As a preliminary step, we study the risk-neutral problem for which an optimal solution exists. This is an extension of initial control system to this type of problem, where the set of admissible controls is convex. An example to carried out to illustrate our main result of risk-sensitive control problem under linear stochastic dynamics with exponential quadratic cost function.

Journal

Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals

Published: Feb 23, 2017

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