Articlegreen2010

Optimality Variational Principle for Controlled Forward-Backward Stochastic Differential Equations with Mixed Initial-Terminal Conditions

139 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 control problem for general coupled forward-backward stochastic differential equations (FBSDEs) with mixed initial-terminal conditions is considered. The control domain is not assumed to be convex, and the control appears in the diffusion coefficient of the forward equation. Necessary conditions of Pontraygin's type for the optimal controls are derived by means of spike variation techniques.

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References

1961Risk, Ambiguity, and the Savage Axioms 1953Le Comportement de l'Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l'Ecole Americaine 1997Backward Stochastic Differential Equations in Finance 1992Stochastic Differential Utility 2002Ambiguity, Risk, and Asset Returns in Continuous Time 1990A General Stochastic Maximum Principle for Optimal Control Problems 1999Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control 1995Solution of forward-backward stochastic differential equations

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2015The Maximum Principle for Global Solutions of Stochastic Stackelberg Differential Games 2013A general maximum principle for optimal control of forward–backward stochastic systems 2013Maximum Principles for Forward-Backward Stochastic Control Systems with Correlated State and Observation Noises 2017Stochastic global maximum principle for optimization with recursive utilities 2018A Global Stochastic Maximum Principle for Fully Coupled Forward-Backward Stochastic Systems

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