Let M be a square integrable martingale indexed by [0, 1]2 with respect to a filtration which possesses the property of conditional independence. Assume that M has trajectories which are continuous for approach from the right upper quadrant and possess limits for the remaining three. M can have...

In this paper we study BSDEs arising from a special class of backward stochastic partial differential equations (BSPDEs) that is intimately related to utility maximization problems with respect to arbitrary utility functions. After providing existence and uniqueness we discuss the numerical...

In this paper we study BSDEs arising from a special class of backward stochastic partial differential equations (BSPDEs) that is intimately related to utility maximization problems with respect to arbitrary utility functions. After providing existence and uniqueness we discuss the numerical...

In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of a forward-backward system (FBSDE) if the generating martingale is a strong Markov process. Then we establish the...

In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of a forward--backward system (FBSDE) if the generating martingale is a strong Markov process. Then we establish the...

In this paper, we consider a security market in which two investors on different information levels maximize their expected logarithmic utility from terminal wealth. While the ordinary investor's portfolio decisions are based on a public information flow, the insider possesses from the beginning...

Double intersection local times [alpha](x,.) of Brownian motion which measure the size of the set of time pairs (s, t), s [not equal to] t, for which Wt and Ws + x coincide can be developed into series of multiple Wiener-Ito integrals. These series representations reveal on the one hand the...

We investigate solutions of backward stochastic differential equations (BSDEs) with time delayed generators driven by Brownian motions and Poisson random measures, that constitute the two components of a Lévy process. In these new types of equations, the generator can depend on the past values...

Let M be a 4N-integrable, real-valued continuous N-parameter strong martingale. Burkholder's inequalities prove to be an adequate tool to control the quadratic oscillations of M and the integral processes associated with it (i.e. multiple 1-stochastic integrals with respect to M and its...