## On the time to ruin for Erlang(2) risk processes.(English)Zbl 1074.91549

The authors consider a Sparre Andersen risk process for which the claim interarrival distribution is Erlang(2). They defined $\varphi(u)= E[e^{-\delta T}1_{\{T< \infty\}}/V(0)= u],$ where $$1_{\{\cdot\}}$$ is the indicator function, $$\delta> 0$$, $$V(t)$$ is the surpluss process. With help of the function $$\varphi(u)$$ the authors find the moments of the time to ruin. It is shown that $$\varphi(u)$$ satisfies some integrodifferential equation. There are also considered two individual claim distributions: an exponential and mixture of two exponentials. For the case of zero initial surplus moments of the time to ruin can be found without an explicit solution for $$\varphi(u)$$, $$u> 0$$.

### MSC:

 91B30 Risk theory, insurance (MSC2010)

### Keywords:

Sparre Andersen risk processes; Erlang(2); Time to ruin

### Citations:

Zbl 0924.60075; Zbl 1028.91556; Zbl 0971.91031
Full Text:

### References:

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