Preprint2011

On Necessary and Sufficient Conditions for Near-Optimal Singular Stochastic Controls

Mokhtar Hafayed · Syed Abbas · Petr Veverka

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

Abstract

This paper is concerned with necessary and sufficient conditions for near-optimal singular stochastic controls for systems driven by a nonlinear stochastic differential equations (SDEs in short). The proof of our result is based on Ekeland's variational principle and some delicate estimates of the state and adjoint processes. This result is a generalization of Zhou's stochastic maximum principle for near-optimality to singular control problem.

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References

1999Stochastic Controls 1990A General Stochastic Maximum Principle for Optimal Control Problems 1995Singular Optimal Stochastic Controls I: Existence 1994The stochastic maximum principle for a singular control problem 1998Stochastic Near-Optimal Controls: Necessary and Sufficient Conditions for Near-Optimality 2001Singular Stochastic Control, Linear Diffusions, and Optimal Stopping: A Class of Solvable Problems 1999A class of solvable singular stochastic control problems 2000Finite-Fuel Singular Control With Discretionary Stopping

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