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...

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...

Let u(t, x), t [epsilon] R, be an adapted process parametrized by a variable x in some metric space X, [mu]([omega], dx) a probability kernel on the product of the probability space [Omega] and the Borel sets of X. We deal with the question whether the Stratonovich integral of u(., x) with...

It has been known that any L log+L-integrable two-parameter martingale M possesses a quadratic variation [M]. We show that the continuity properties of M are inherited by its quadratic variation. If M has no point jumps, [M] has no point jumps. [M] has at most axial jumps with respect to one of...

We consider backward stochastic differential equations (BSDEs) with nonlinear generators typically of quadratic growth in the control variable. A measure solution of such a BSDE will be understood as a probability measure under which the generator is seen as vanishing, so that the classical...