Inria / Raweb 2004
Team: Mathfi

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Team : mathfi

Section: New Results

Keywords: information, control.

Anticipative stochastic optimal control

Participant: D. Lefèvre.

The stochastic maximum principle is a powerful tool to characterize optimal control processes for a controlled system of stochastic differential equations. Control processes represent the policy of the decision-makers and are usually assumed nonanticipative. In this work, we waive this adaptation constraint and allow the policies to be adapted to a larger filtration that the one generated by the Brownian motion which drives the controlled stochastic differential equation. First, we show how to correctly define a unique solution for our resulting anticipative controlled system. Next, we derive a Pontryagin-type maximum principle for possibly anticipative optimal stochastic controls where the definition of the Hamiltonian is substantially modified.