Rises of nonnegative semimartingales

No Arbitrage without Semimartingales

We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are possible in our setting, for example fractional Brownian motion.

Smoothing Signals for Semimartingales

From Diffusions to Semimartingales

This chapter is a quick review of the theory of semimartingales, these processes being those for which statistical methods are considered in this book. A process is a collection X = (Xt) of random variables with values in the Euclidean space R for some integer d ≥ 1, and indexed on the half line R+ = [0,∞), or a subinterval of R+, typically [0, T ] for some real T > 0. The distinctive feature h...

Information and Semimartingales

Stochastic Analysis provides methods to describe random numerical processes. The descriptions depend strongly on the underlying information structure, which is represented in terms of filtrations. The first part of this thesis deals with impacts of changes in the information structure on the appearance of a stochastic process. More precisely, it analyses the consequences of a filtration enlarge...

Some norm estimates for semimartingales

In this paper we introduce a new type of norm for semimartingales. Our norm is defined in the spirit of quasimartingales, and it characterizes square integrable semimartingales. This work is motivated by our study of zero-sum stochastic differential games, whose value process we conjecture to be a semimartingale under a class of probability measures under some conditions. The norm introduced he...