Actuarial Seminar: Prof. Dmitry Korshunov (University of Lancaster)

Abstract: We consider a random walk S_n with a finite positive drift that is stopped at a random time tau having intermediate regularly varying distribution. We assume that the jump distribution is lighter than that of $\tau$. Under these conditions we show that the distributions of S_{tau} and of  M_{tau} = max_{k <= tau} S_k are tail equivalent and their common tail asymptotics are determined by that of tau, while S_n only contributes via the law of large numbers. We consider the two cases, where $\tau$ is a random time independent of the future increments of the random walk or tau is arbitrary dependent of S_n.

In the course of the talk we will discuss why quite often the class of intermediate regularly varying distributions is more appropriate than the class of regularly varying distributions. We will also discuss in detail the importance of the notion of a random time independent of the future, which includes both stopping times and independent times.

Joint work with S. Foss (Edinburgh).

Seminar organized by Professor E. Hashorva.