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 \(\varphi(u)\), \(u> 0\).


91B30 Risk theory, insurance (MSC2010)
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