Events

Two Exponential Functionals of Levy Processes

Seminar / Lecture
 
For NYU Community

You are cordially invited to attend the FRE Lecture Series on Tuesday, September 27th at 3PM in LC 400.

Dr. Daniel Dufresne, Professor in the Department of Mathematics and Statistics at the University of Montreal, and then the Centre for Actuarial Studies at the University of Melbourne, Australia will present a talk on:

Title: Two exponential Functionals of Levy Processes

Abstract: The talk has two parts. The first part (with Prof. F. Vazquez-Abad, CUNY) is about efficient pricing of average (or “Asian”) options. There are many known results about the continuous average of geometric Brownian motion, but relatively few about the more realistic case of discrete averages. It will be shown that excellent precision is obtained by properly adjusting the distribution of lower-dimensional averages, implying significantly shorter computation times. The second part (with Z. Zhang, PhD student) is about models where i.i.d. claims {C(k)} are paid at renewal times {T(k)}, for example in insurance. Of practical interest is the distribution of Z(t), the discounted value of claims occurring over the period [0,t].  New results on how to find the distribution of Z(t) will be presented. An important tool (previously applied by Marc Yor to continuous average Asian options) is the Laplace transform w.r.t. to time (“t”) of the process {Z(t)}.

Bio: After studies in Mathematics and a short period in actuarial consulting, Daniel Dufresne was Professor in the Dept. of Mathematics and Statistics at the University of Montreal, and then Professor in the Centre for Actuarial Studies at the University of Melbourne (Australia), where he has been since 2003. His interests are in probability theory and financial mathematics, in particular properties and approximation of probability distributions, option pricing and computing.


Light refreshments will be served.