MATHEMATICS

Asymptotic Expansions of the Ruin Probability for a Generalized Poisson Process

A. T. Semenov

Novosibirsk State University for Economics and Management

Abstract: Let $\xi(t)$, $t\geqslant0,$ be a generalized Poisson process, and let $\tau(x)=\inf\{t:\xi(t)\geqslant x\}, x>0$. The complete asymptotic expansions of the distribution $\tau(x)$ are obtained for $x\to\infty$ under Cramér type condition.

Keywords: generalized Poisson process, ruin probability, Laplace-Stieltjes transform, factorization method, asymptotic expansion.

UDC: 519.21


Accepted: October 16, 2008