Journal
ASTIN BULLETIN
Volume 35, Issue 1, Pages 145-161Publisher
PEETERS
DOI: 10.1017/S0515036100014100
Keywords
phase-type distribution; ruin probability; EM-algorithm; Markov chain Monte Carlo
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Phase-type distributions, defined as the distributions of absorption times of certain Markov jump processes, constitute a class of distributions on the positive real axis which seems to strike a balance between generality and tractability. Indeed, any positive distribution may be approximated arbitrarily closely by phase-type distributions whereas exact solutions to many complex problems in stochastic modeling can be obtained either explicitly or numerically. In this paper we introduce phase-type distributions and retrieve some of their basic properties through appealing probabilistic arguments which, indeed, constitute their main feature of being mathematically tractable. This is illustrated in an example where we calculate the ruin probability for a rather general class of surplus processes where the premium rate is allowed to depend on the current reserve and where claims sizes are assumed to be of phase-type. Finally we discuss issues concerning statistical inference for phase-type distributions and related functionals such as e.g. a ruin probability.
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