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The probability of ruin in finite time with discrete claim size distribution. (English) Zbl 0926.62103
Summary: 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 \(P(T>x)\).

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
60G35 Signal detection and filtering (aspects of stochastic processes)
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