Large deviation limit for discrete-time, totally observed stochastic control problems with multiplicative cost

We show that a large class of discrete-time dynamic games can be obtained as a limit of stochastic control problems with multiplicative cost. Our approach consists in analyzing the large deviation properties of the Markov kernels associated with the stochastic dynamics, and allows us to give a unitary treatment of several nonlinear models.     

Maximum principle for optimal control problems involving impulse controls with nonsmooth data

This paper is concerned with the stochastic maximum principle for impulse optimal control problems of forward–backward systems, where the coefficients of the forward part are Lipschitz continuous. The domain of the regular controls is not necessarily convex. We establish a Pontryagins maximum principle for this control problem by applying Ekelands variational principle to a sequence of approximated control problems with smooth coefficients of the initial problems.     

PROMISE: A DSS for multiple objective stochastic linear programming problems

Most of the multiple objective linear programming (MOLP) methods which have been proposed in the last fifteen years suppose deterministic contexts, but because many real problems imply uncertainty, some methods have been recently developed to deal with MOLP problems in stochastic contexts. In order to help the decision maker (DM) who is placed before such stochastic MOLP problems, we have built a Decision Support System called PROMISE. On the one hand, our DSS enables the DM to identify many current stochastic contexts: risky situations and also situations of partial uncertainty. On the other hand, according to the nature of the uncertainty, our DSS enables the DM to choose the most appropriate interactive stochastic MOLP method among the available methods, if such a method exists, and to solve his problem via the chosen method.     

Stochastic Optimal Control for the Stochastic Heat Equation with Exponentially Growing Coefficients and with Control and Noise on a Subdomain

Abstract

We consider stochastic optimal control problems in Banach spaces, related to nonlinear controlled equations with dissipative non linearities: on the nonlinear term we do not impose any growth condition. The problems are treated via the backward stochastic differential equations approach, that allows also to solve in mild sense Hamilton Jacobi Bellman equations in Banach spaces. We apply the results to controlled stochastic heat equation, in space dimension 1, with control and noise acting on a subdomain.     

Meshfree Approximation for Stochastic Optimal Control Problems

In this work,we study the gradient projection method for solving a class of stochastic control problems by using a mesh free approximation ap-proach to implement spatial dimension approximation.Our main contribu-tion is to extend the existing gradient projection method to moderate high-dimensional space.The moving least square method and the general radial basis function interpolation method are introduced as showcase methods to demonstrate our computational framework,and rigorous numerical analysis is provided to prove the convergence of our meshfree approximation approach.We also present several numerical experiments to validate the theoretical re-sults of our approach and demonstrate the performance meshfree approxima-tion in solving stochastic optimal control problems.