Explicit expressions for the ruin probabilities of Erlang risk processes with Pareto individual claim distributions. (English) Zbl 1054.62129
The risk process in which claim arrival times have an Erlang distribution and the claim size follows a Pareto distribution is considered. An explicit expression for the probability of ruin \(\Psi(n)\) is given. It is shown that \(\Psi(n)\) can be expressed as the sum of expected values of functions of gamma random variables. Numerical examples of the main results are given.
Reviewer: Andrew Olenko (Kyïv)
MSC:
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 91B30 | Risk theory, insurance (MSC2010) |
Keywords:
ruin probability; Erlang process; Pareto distribution; Laplace transform; removable singularity; contour integrationReferences:
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