Marc Yor, born on 24 July 1949, passed away on 9 January 2014. After studies at École Normale Supérieure de Cachan (1969-1973), he held a position at CNRS and was Professor at the Université Pierre et Marie Curie (Paris 6) from 1981 to January 2014, when he retired.
He was a member of the Académie des Sciences in the Mathematical Section and a member of the Institut Universitaire de France.
He was a recipient of several awards, including the Humboldt Prize, the Montyon Prize of the Académie des Sciences, and was awarded the Ordre National du Mérite by the French Republic.
His PhD dissertation on integral representation theorems for martingales and extremal distributions was under the supervision of Pierre Priouret, and was defended in 1976.
Marc was interested in many areas of probability theory and stochastic processes, including Brownian motion and Bessel processes. He published more than 400 papers with about 100 co-authors, wrote fourteen books, among them the seminal book on continuous martingales (Revuz and Yor 1991, first edition), and had 40 PhD students.
He was greatly inspired by Financial Mathematics and, among other problems, studied the pricing of double barrier options, the law of the integral of a geometric Brownian motion (to find the Asian option price in closed form), a new interpretation of the Black-Scholes formula for European options, and the distribution of Brownian quantiles. He introduced the use of change of time in finance, in particular, to exhibit interesting Lévy processes such as the CGMY model. The study of martingales with given marginals led him to the «peacock» developments. Marc organized two conferences at the Académie des Sciences in 2005 and 2008 on Mathematical Finance.
He was always trying to «truly» understand Brownian motion. He discovered links among various properties that were hidden to other people such as the link between first/last passage times and the Black-Scholes formula. The starting point of this adventure (see his book on option prices as probabilities) was that, under an adequate choice of parameters, the price of a call is equal to P(|B1|< 1/4), which is linked with the probability of a first passage time being greater than 1. Who else would have been able to understand the deep structure in that obvious result? He was for us like a magician – able to show us that there are colors in the black and white picture we were looking at. Marc Yor was well-known for his humility, modesty, enthusiasm and kindness. He was invariably ready to share his knowledge with anyone seeking his help. He was an extraordinary teacher and speaker, giving listeners the impression that his results were simple. His brilliance was marked by an uncanny ability and perseverance to not only keep asking the next question, but invariably following through with the answer. Watching him work was a delightful inspiration to those who had the opportunity to do so.
We lost an exceptional mathematician, a wonderful human being and extraordinary man, who influenced many lives.
