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Computational methods in risk theory: a matrix-algorithmic approach. (English) Zbl 0748.62058
The paper discusses and shows the probabilities of ruin, \(\psi(u)\), obtained from fitting a selection of conditional claim amount distributions by phase-type distributions. The matrix-algorithmic method, initially due to Neuts, and associated with the latter distributions, when carried over to a continuous-state setting, provides computationally tractable solutions for \(\psi(u)\); the example of the compound Poisson distribution is particularly elegant as evidenced by the application to hyperexponential claims. Other examples illustrated are for the Sparre Andersen process, Markov modulated arrivals, and periodic Poisson processes.
Reviewer: G.Lord (Princeton)

62P05 Applications of statistics to actuarial sciences and financial mathematics
65C99 Probabilistic methods, stochastic differential equations
91B30 Risk theory, insurance (MSC2010)
Full Text: DOI
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