Beneš condition for a discontinuous exponential martingale

An Exponential Martingale Equation

We prove an existence of a unique solution of an exponential martingale equation in the class of BMO martingales. The solution is used to characterize optimal martingale measures.

On Zhao-Woodroofe’s condition for martingale approximation∗

The Zhao-Woodroofe condition has been introduced in [19] and it is a necessary and sufficient condition for the existence of a martingale approximation of a causal stationary process. Here, a nonadapted version is given and the convergence of Cesaro averages is replaced by a convergence of a subsequence. The nonadapted version is of a different form than in other cases, e.g. of Wu-Woodroofe or ...

Martingale Inequalities in Exponential Orlicz Spaces

A result is found which is similar to BDG-inequalities, but in the framework of exponential (non moderate) Orlicz spaces. A special class of such spaces is introduced and its properties are discussed with respect to probability measures, whose densities are connected by an exponential model. Acknowledgement: Thanks are due to Prof. M. Mania (Georgian Academy of Sciences) for the discussions and...

Minimal F Q - Martingale Measures for Exponential Lévy Processes

Let L be a multidimensional Lévy process under P in its own filtration. The f-minimal martingale measure Qq is defined as that equivalent local martingale measure for E(L) which minimizes the f-divergence E [ (dQ/dP ) ] for fixed q ∈ (−∞, 0) ∪ (1,∞). We give necessary and sufficient conditions for the existence of Qq and an explicit formula for its density. For q = 2, we relate the sufficient c...

A Sufficient Condition for Exponential Dichotomy of Parabolic Evolution Equations