Plenary Lecture

Fractional Randomness and Implied Fractional Hazard Rate

Professor Pierre Vallois
Université de Lorraine
Institut Elie Cartan de Lorraine

Abstract: The purpose of the talk is to consider an application of fractional calculus to define fractional density functions (resp. fractional cumulative distribution functions). We provide a number of results, defining the functional forms of these distributions as well as their existence. We also deal with fractional hazard rates which extend default probability distributions. We interpret these new concepts in terms of classical probabilistic tools. Examples are given to motivate the usefulness of a statistical approach to fractional calculus and its application to economic and financial problems.

Brief Biography of the Speaker: Dr. Pierre Vallois is full Professor in mathematics at Université de Lorraine, Nancy, since 1996. He received the Ph.D. degree and the “thèse d’état” in 1981 and 1990, respectively, from the university Pierre et Marie Curie (Paris VI). He served as researcher at CNRS (Laboratoire de Probabilités et Applications, University of Paris VI) from 1984 to 1993. He was the manager of the Probability and Statistics group from 1996 to 2009 and at the head of the Mathematical Department of the Faculty of Sciences and Technologies of Nancy, Université de Lorraine (2009-2013). He is presently the director of the research structure called Fédération Charles Hermite from 2013. He is a member of the editorial board of the journal Risk and Decision Analysis (2008-present). He organized six main meetings in probability theory at Nancy and two meetings with corporates in Lorraine (in the setting of the Fédération Charles Hermite). He supervised eleven thesis and two are in progress. From 2005, he visited Polytechnic University of New-York, Turku University (Finland), Marrakech (Marocco), Monastir (Tunisia), Potsdam (2013) … and gave 28 talks in international meetings. 106 papers have been published in peer review journals. His current interests include stochastic processes, generalized stochastic calculus, modelling in biology, medicine and finance.

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