Jean-Michel Courtault

Louis Bachelier on the Centenary of "Théorie de la Spéculation"

Written on the occasion of the centenary of Louis Bacheliers 1900 PhD thesis “Theorie de la speculation”, 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 Bacheliers difficult personal and scientific career. This includes a discussion of Poincares report on the PhD thesis (the report itself with an English translation is reproduced in the appendix), and an explanation for the controversy between Bacheliers work and Paul L´evys reports on it. The paper also contains a curriculum vitae and a list of the publications of Bachelier is made available.

On the law of one price

Abstract.We consider the standard discrete-time model of a frictionless financial market and show that the law of one price holds if and only if there exists a martingale density process with strictly positive initial value. In contrast to the classical no-arbitrage criteria, this density process may change its sign. We also give an application to the CAPM.

Local risk aversion in the rank dependent expected utility model: First order versus second order effects

Abstract We evaluate locally the risk premium of a lottery in the framework of the RDEU model as the sum of two terms. The first is a measure of risk aversion, while the second is a measure of spreading aversion.

A NOTE ON LUENBERGER'S ZERO-MAXIMUM PRINCIPLE FOR CORE ALLOCATIONS

In this note, we state a zero-maximum principle for core allocations, a result which was foreseen by Luenberger (1995). We prove a generalization of the first-zero maximum theorem of Luenberger. Roughly said, an allocation is in the core if for every coalition, the sum of individual benefit functions is non-positive. We also provide some partial converses which give a generalization of the second-zero maximum theorem of Luenberger.