Maximum Principle for Stochastic Control of SDEs with Measurable Drifts

A maximum principle for relaxed stochastic control of linear SDEs with application to bond portfolio optimization

We study relaxed stochastic control problems where the state equation is a one dimensional linear stochastic differential equation with random and unbounded coefficients. The two main results are existence of an optimal relaxed control and necessary conditions for optimality in the form of a relaxed maximum principle. The main motivation is an optimal bond portfolio problem in a market where th...

Stochastic Maximum Principle for Hilbert Space Valued Forward-Backward Doubly SDEs with Poisson Jumps

Maximum Principle for Singular Stochastic Control Problems

In this paper, an optimal singular stochastic control problem is considered. For this model, it is obtained a general stochastic maximum principle by using a time transformation. This is the first version of the stochastic maximum principle that covers the singular control problem in the nonlinear case.

Stochastic Flows of Sdes with Irregular Drifts and Stochastic Transport Equations

Abstract. In this article we study (possibly degenerate) stochastic differential equations (SDE) with irregular (or discontiuous) drifts, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere stochastic invertible flow associated with the SDE in the sense of Lebesgue measure. In the case of constant diffusions and BV drifts, we obtain such a result...

Weak differentiability of solutions to SDEs with semi-monotone drifts

‎In this work we prove Malliavin differentiability for the solution to an SDE with locally Lipschitz and semi-monotone drift‎. ‎To prove this formula‎, ‎we construct a sequence of SDEs with globally Lipschitz drifts and show that the $p$-moments of their Malliavin derivatives are uniformly bounded‎.