## Abstract

In this paper we first consider a risk process in which claim inter-arrival times and the time until

the first claim have an Erlang (2) distribution. An explicit solution is derived for the probability of ultimate

ruin, given an initial reserve of u when the claim size follows a Pareto distribution. Follow Ramsay[8], Laplace

transforms and exponential integrals are used to derive the solution, which involves a single integral of real

valued functions along the positive real line, and the integrand is not of an oscillating kind. Then we show

that the ultimate ruin probability can be expressed as the sum of expected values of functions of two different

Gamma random variables. Finally, the results are extended to the Erlang(n) case. Numerical examples are

given to illustrate the main results.

the first claim have an Erlang (2) distribution. An explicit solution is derived for the probability of ultimate

ruin, given an initial reserve of u when the claim size follows a Pareto distribution. Follow Ramsay[8], Laplace

transforms and exponential integrals are used to derive the solution, which involves a single integral of real

valued functions along the positive real line, and the integrand is not of an oscillating kind. Then we show

that the ultimate ruin probability can be expressed as the sum of expected values of functions of two different

Gamma random variables. Finally, the results are extended to the Erlang(n) case. Numerical examples are

given to illustrate the main results.

Original language | English |
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Pages (from-to) | 495-506 |

Journal | Acta Mathematicae Applicatae Sinica |

Volume | 20 |

Issue number | 3 |

Publication status | Published - 2004 |

Externally published | Yes |