A General Optimality Conditions for Stochastic Control Problems of Jump Diffusions

We consider a stochastic control problem where the system is governed by a non linear stochastic differential equation with jumps. The control is allowed to enter into both diffusion and jump terms. By only using the first order expansion and the associated adjoint equation, we establish necessary a...

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Bibliographic Details
Published in:Applied mathematics & optimization 2012-02, Vol.65 (1), p.15-29
Main Authors: Bahlali, Seid, Chala, Adel
Format: Article
Language:English
Subjects:
Adjoints
Brownian motion
Calculus of Variations and Optimal Control
Optimization
CONTROL
Control equipment
Control systems
DIFFERENTIAL EQUATIONS
DIFFUSION
Inequality
Mathematical analysis
Mathematical and Computational Physics
MATHEMATICAL METHODS AND COMPUTING
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
NONLINEAR PROBLEMS
Numerical and Computational Physics
Optimization
Random variables
Simulation
STOCHASTIC PROCESSES
Stochasticity
Studies
Systems Theory
Theoretical
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Summary:We consider a stochastic control problem where the system is governed by a non linear stochastic differential equation with jumps. The control is allowed to enter into both diffusion and jump terms. By only using the first order expansion and the associated adjoint equation, we establish necessary as well as sufficient optimality conditions of controls for relaxed controls, who are a measure-valued processes.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-011-9143-z