Course duration: 3 h
Stochastic processes are not only mathematically rich objects. They also have an extensive range of applications in, e.g., physics, engineering, ecology, and economics - indeed, it is difficult to conceive of a quantitative discipline in which they do not feature. There is a limited amount that can be said about the general concept, and much of both theory and applications focuses on the properties of specific classes of process that possess additional structure. Many of these, such as random walks and Markov chains, will be well known to most of us. Others, such as semimartingales and measure-valued diffusions, are more esoteric. We will give an introduction to a class of stochastic processes called Levy processes, in honor of the great French
probabilist Paul Levy, who rst studied them in the 1930s.
This course will cover some basic definitions and examples of Levy processes. We will discuss very powerful, but not really useful theorem by Levy and Khintchine and try to understand the structure with the help of Levy-Ito decomposition.
We apply Levy processes in insurance and financial mathematics almost all the time. I want to give some examples during this course: compound poisson process is well known in actuarial science, and NIG processes are used in option pricing.
Mr. Illia Simonov
Place of employment: University of Leoben