ESSENTIAL SUPREMUM WITH RESPECT TO A RANDOM PARTIAL ORDER

Inspired by the theory of nancial markets with transaction costs, we study a concept of essential supremum in the framework where a random partial order in Rd is lifted to the space L0(Rd) of d-dimensional random variables. In contrast to the classical de nition, we de ne the essential supremum as a subset of random variables satisfying some natural properties. An application of the introducednotion to a hedging problem under transaction costs is given

Louis Bachelier On the centenary of Théorie de la Spéculation

International audienceWritten on the occasion of the centenary of Louis Bachelier's 1900 PhD thesis “Théorie de la spéculation”, this paper puts Bachelier into a historical perspective. It explains his role as a pioneer in both mathematical finance and probability theory, and it also gives a careful account of Bachelier's difficult personal and scientific career. This includes a discussion of Poincaré's report on the PhD thesis (the report itself with an English translation is reproduced in the appendix), and an explanation for the controversy between Bachelier's work and Paul L´evy's reports on it. The paper also contains a curriculum vitae and a list of the publications of Bachelier is made available

On supremal and maximal sets with respect to random partial orders.

The paper deals with definition of supremal sets in a rather general framework where deterministic and random preference relations (preorders) and partial orders are defined by continuous multi-utility representations. It gives a short survey of the approach with some new results on maximal sets

On Supremal and Maximal Sets with Respect to Random Partial Orders

The paper deals with de nition of supremal sets in a rather general frameworkwhere deterministic and random preference relations (preorders) and partialorders are de ned by continuous multi-utility representations. It gives ashort survey ofnonnonouirechercheInternationa