Abstract
This paper establishes some enlightening connections between the explicit formulas of the finite-time ruin probability obtained by Ignatovand Kaishev (2000, 2004) and Ignatov et al. (2001) for a risk model allowing dependence. The numerical properties of these formulas are investigated and efficient algorithms for computing ruin probability with prescribed accuracy are presented. Extensive numerical comparisons and examples are provided.
Highlights
Research on ruin probability beyond the classical risk model has intensified in recent years
Asymptotic exponential estimates for both finite and infinite time ruin probabilities are obtained for light-tail claims, using Laplace transform
In the context of ruin theory classical Appell polynomials first appear in Ignatov and Kaishev (2000). It has been shown by Ignatov and Kaishev (2000, 2004) that the occurrence of classical Appell polynomials, Ak(x), in the ruin formulas (1) (through the determinants bj(.)) and (4) is related to the fact that, given Nx = k, the random vector of claim arrival times T1, . . . , Tk coincides in distribution with the order statistics of k independent uniformly distributed on [0, x] random variables
Summary
Research on ruin probability beyond the classical risk model has intensified in recent years. A collective finite-horizon ruin probability model with Poisson claim arrivals, dependent discrete claim amounts having any joint distribution but independent of the claim arrival times, and aggregate premium income represented by any non-decreasing positive, real valued function, has been considered by Ignatov and Kaishev (2000). They give an explicit finite-horizon ruin probability formula in terms of infinite sums of determinants which are shown by the authors to admit representation as classical Appell polynomials.
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