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 deal with the utility maximization problem with general utility functions including power utility with liability. We derive a new approach in which we reduce the resulting control problem to the study of a system of fully-coupled Forward–Backward Stochastic Differential...

We consider financial markets with agents exposed to an external source of risk which cannot be hedged through investments on the capital market alone. The sources of risk we think of may be weather and climate. Therefore we face a typical example of an incomplete financial market. We design a...

Let M be a 4N-integrable, real-valued continuous N-parameter strong martingale. By extending Itô-type formulas for M to a function whose 2Nth derivative is Dirac's [delta]-distribution, Tanaka-type formulas for M are obtained. They represent local time of M with respect to occupation time...

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 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...