Given a càdlàg process X on a filtered measurable space, we construct a version of its
semimartingale characteristics which is measurable with respect to the underlying …

Every submartingale S of class D has a unique Doob–Meyer decomposition S= M+ A, where
M is a martingale and A is a predictable increasing process starting at 0. We provide a short …

This paper establishes a non-stochastic analog of the celebrated result by Dubins and
Schwarz about reduction of continuous martingales to Brownian motion via time change. We …

A wealth-process set is abstractly defined to consist of nonnegative càdlàg processes
containing a strictly positive semimartingale and satisfying an intuitive re-balancing property …

A financial market model where agents trade using realistic combinations of simple (ie, finite
combinations of buy-and-hold) no-short-sales strategies is considered. Minimal assumptions …

The present lecture notes are based on several advanced courses which I gave at the
University of Vienna between 2011 and 2013. In 2015 I gave a similar course (“Nachdiplom …

Stricker's theorem states that a Gaussian process is a semimartingale in its natural filtration if
and only if it is the sum of an independent increment Gaussian process and a Gaussian …

For a continuous function f∈C(0,1), define the Vervaat transform V(f)(t):=f(τ(f)+t\mod1)+f(1)
1_{t+τ(f)≧1\}-f(τ(f)), where τ(f) corresponds to the first time at which the minimum of f is …

In the spirit of Koml\'os's theorem, we investigate when a sequence of semimartingales
satisfying a boundedness condition admits forward convex combinations converging in …

We give a new proof of the celebrated Bichteler–Dellacherie theorem, which states that a
process S is a good integrator if and only if it is the sum of a local martingale and a finite …