In this paper, we study backward stochastic differential equations (BSDEs) with respect to general filtrations. We prove existence and uniqueness theorems for such BSDEs and we establish a comparison theorem. Reflected ...

We give a short introduction to the stochastic calculus for Itô-Lévy processes and review briefly the two main methods of optimal control of systems described by such processes: (i) Dynamic programming and the ...

We study optimal stochastic control problems with jumps under model uncertainty. We rewrite such problems as stochastic differential games of forward–backward stochastic differential equations. We prove general stochastic ...

We consider a financial market model with a single risky asset whose price process evolves according to a general jump-diffusion with locally bounded coefficients and where market participants have only access to a partial ...

We study stochastic differential games of jump diffusions driven by Brownian motions and compensated Poisson random measures, where one of the players can choose the stochastic control and the other player can decide when ...

This paper is mainly a survey of recent research developments regarding methods for risk minimization in financial markets modeled by Itô-Lévy processes, but it also contains some new results on the underlying stochastic ...

The single auction equilibrium of Kyle’s (1985) is studied, in which noise traders may be partially informed, or alternatively they can be manipulated. Unlike Kyle’s assumption that the quantity traded by the noise traders ...

We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. ...

We study partial information, possibly non-Markovian, singular stochastic control of Itô--Lévy processes and obtain general maximum principles. The results are used to find connections between singular stochastic control, ...

We consider general singular control problems for random fields given by a stochastic partial differential equation (SPDE). We show that under some conditions the optimal singular control can be identified with the solution ...