We study a constrained optimal control problem allowing for degenerate coefficients. The coefficients can be random and then the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singular terminal condition. For this degenerate BSPDE, we...

We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of...

We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a...

Backward stochastic Riccati equations are motivated by the solution of general linear quadratic optimal stochastic control problems with random coefficients, and the solution has been open in the general case. One distinguishing difficult feature is that the drift contains a quadratic term of...

A local strict comparison theorem and some converse comparison theorems are proved for reflected backward stochastic differential equations under suitable conditions.

We study dynamic monetary risk measures thatdepend on bounded discrete-time processesdescribing the evolution of financial values. The time horizoncan be finite or infinite. We call a dynamic risk measuretime-consistent if it assigns to a process of financialvalues the same risk irrespective of...

Let X be an R^d-valued special semimartingale on a probability space with canonical decomposition X=X_0+M+A. Denote by G_T(Theta) the space of all random variables (theta bullet X)_T, where theta is a predictable X- integrable process such that the stochastic integral theta bullet X is in the...