Nacira Agram

Malliavin Calculus and Optimal Control of Stochastic Volterra Equations

Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore, classical methods, such as dynamic programming, cannot be used to study optimal control problems for such equations. However, we show that using Malliavin calculus, it is possible to formulate modified functional types of maximum principle suitable for such systems. This principle also applies to situations where the controller has only partial information available to base her decisions upon. We present both a Mangasarian sufficient condition and a Pontryagin-type maximum principle of this type, and then, we use the results to study some specific examples. In particular, we solve an optimal portfolio problem in a financial market model with memory.

Infinite horizon optimal control of forward-backward stochastic differential equations with delay

We consider a problem of optimal control of an infinite horizon system governed by forward-backward stochastic differential equations with delay. Sufficient and necessary maximum principles for optimal control under partial information in infinite horizon are derived. We illustrate our results by an application to a problem of optimal consumption with respect to recursive utility from a cash flow with delay.

Optimal control of forward–backward mean-field stochastic delayed systems

We study methods for solving stochastic control problems of systems offorward–backward mean-field equations with delay, in finite and infinite time horizon.Necessary and sufficient maximum principles under partial information are given. The results are applied to solve a mean-field recursive utility optimal problem.