Articlehybrid2012

Necessary Conditions for Optimal Control of Forward-Backward Stochastic Systems with Random Jumps

21 citations0/0 files storedInternational Journal of Stochastic Analysis

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

Abstract

This paper deals with the general optimal control problem for fully coupled forward-backward stochastic differential equations with random jumps (FBSDEJs). The control domain is not assumed to be convex, and the control variable appears in both diffusion and jump coefficients of the forward equation. Necessary conditions of Pontraygin's type for the optimal controls are derived by means of spike variation technique and Ekeland variational principle. A linear quadratic stochastic optimal control problem is discussed as an illustrating example.

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References

1976Option pricing when underlying stock returns are discontinuous 1983Stochastic Differential Equations and Diffusion Processes 2003Financial Modelling with Jump Processes 1997Backward Stochastic Differential Equations in Finance 1990A General Stochastic Maximum Principle for Optimal Control Problems 2007Forward-Backward Stochastic Differential Equations and their Applications 1994Necessary Conditions for Optimal Control of Stochastic Systems with Random Jumps 1940Science in China

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