Article2002

Generalized Solutions in Nonlinear Stochastic Control Problems

22 citations0/0 files storedSIAM Journal on Control and Optimization

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Optimization and Variational Analysis

Abstract

An optimal stochastic control problem is considered for systems with unbounded controls satisfying an integral constraint. It is shown that there exists an optimal control within the class of generalized controls leading to impulse actions. Applying an approach of time transformation, developed recently for deterministic systems, the original control problem is shown to be equivalent to an optimal stopping problem. Moreover, the description of generalized solutions is given in terms of stochastic differential equations governed by a measure.

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2007Brownian Motion and Stochastic Calculus 1999Continuous Martingales and Brownian Motion 2005Stochastic Integration and Differential Equations 1998Brownian Motion and Stochastic Calculus 1976Stochastic Differential Equations and Applications 1980Controlled Diffusion Processes 1990Stochastic Integration and Differential Equations 1986Stochastic Calculus and Applications.

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