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 coupled forward–backward stochastic differential system (FBSDS) is formulated in spaces of fields for the incompressible Navier–Stokes equation in the whole space. It is shown to have a unique local solution, and further if either the Reynolds number is small or the dimension of the...

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

Using the Ito differentiation rule, the properties of stochastic flows and the unique decomposition of special seminartingales, the integrand in a stochastic integral is quickly identified.

We construct a bond-stock market composed of d stocks and many bonds with jumps driven by general marked point process as well as by an ℝn-valued Wiener process. By composing these tools we introduce the concept of a compatible bond-stock market and give a necessary and sufficient condition...

We consider a financial market in which the discounted price process S is an ℝd-valued semimartingale with bounded jumps, and the variance-optimal martingale measure (VOMM) Qopt is only known to be a signed measure. We give a backward semimartingale equation (BSE) and show that the density...

We apply theoretical results by Peng on supersolutions for Backward SDEs (BSDEs) to the problem of finding optimal superhedging strategies in a generalized Black–Scholes market under constraints. Constraints may be imposed simultaneously on wealth process and portfolio. They may be non-convex,...

We consider the mean-variance hedging of a contingent claim H when the discounted price process S is an [image omitted]-valued quasi-left continuous semimartingale with bounded jumps. We relate the variance-optimal martingale measure (VOMM) to a backward semimartingale equation (BSE) and show...

We consider an optimal control problem for an Itô diffusion and a related stopping problem. Their value functions satisfy (d/dx)V=u and an optimal control defines an optimal stopping time. Conversely, we construct an optimal control from optimal stopping times, find a representation of V as an...

We provide a method for solving dynamic expected utility maximization problems with possibly not everywhere increasing utility functions in an Lp-semimartingale setting. In particular, we solve the problem for utility functions of type (exponential problem) and (2m-th problem). The convergence...