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Duality and Approximation of Stochastic Optimal Control Problems Under Expectation Constraints by Pfeiffer, Laurent; Tan, Xiaolu; Zhou, Yulong is a scholarly article available to read on EtoBox.

What is Duality and Approximation of Stochastic Optimal Control Problems Under Expectation Constraints about?

We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is in duality with an optimization problem involving the Lagrange multiplier associated with the constraints. Then by convex analysis techniques, we provide a general existence result and some a priori estimation of the dual optimizers. We further provide a necessary and sufficient optimality condition for the initial constrained control problem. The same results are also obtained for a discrete time constrained control problem. Moreover, under additional regularity conditions, it is proved that the discrete time control problem converges to the continuous time problem, possibly with a convergence rate. This convergence result can be used to obtain numerical algorithms to approximate the continuous time control problem, which we illustrate by two simple numerical examples.

Author

Pfeiffer, Laurent; Tan, Xiaolu; Zhou, Yulong

Published

2020

Language

EN