The probability of ruin in finite time with discrete claim size distribution

Abstract

The ruin time T is considered as the time of first crossing between a compound Poisson trajectory and an upper increasing boundary. Under the assumption that the claim sizes are integer-valued, we show that the distribution of T can be expressed in terms of generalized Appell polynomials. Using the algebraic properties of these polynomials elegant expressions are obtained for P(T > x).

Key words:

• First crossing
• compound Poisson process
• upper increasing boundary
• generalized Appell polynomials