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...

This article presents new results on the problem of selecting (online) a monotone subsequence of maximum expected length from a sequence of i.i.d. random variables. We study the case where the variables are observed sequentially at the occurrence times of a Poisson process with known rate. Our...

This article provides a refinement of the main results for the monotone subsequence selection problem, previously obtained by Bruss and Delbaen (Stoch. Proc. Appl. 96 (2001) 313). Let (Ns)s[greater-or-equal, slanted]0 be a Poisson process with intensity 1 defined on the positive half-line. Let...

If the random future evolution of values is modelled in continuous time, then a risk measure can be viewed as a functional on a space of continuous-time stochastic processes. We extend the notions of coherent and convex monetary risk measures to the space of bounded càdlàg processes that are...

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.

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...

We consider a general stochastic model of frictionless continuous trading. The price process is a semimartingale and the model is incomplete. Our objective is to hedge contingent claims by using trading strategies with a small riskiness. To this end, we introduce a notion of local R-minimality...

Let L be a multidimensional Lévy process under P in its own filtration and consider all probability measures Q turning L into a local martingale. The minimal entropy martingale measure QE is the unique Q which minimizes the relative entropy with respect to P. We prove that L is still a Lévy...