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In this paper, we generalise the results presented in the literature for theruin probability for the insurer--reinsurer model under a pro-rata reinsurancecontract. We consider claim amounts that are described by a phase-typedistribution that includes exponential, mixture of exponential, Erlang, andmixture of Erlang distributions. We derive the ruin probability formulas withthe use of change-of-measure technique and present important special cases. Weillustrate the usefulness of the introduced model by fitting it to thereal-world loss data. With the use of statistical tests and graphical tools, weshow that the mixture of Erlangs is well-fitted to the data and is superior toother considered distributions. This justifies the fact that the presentedresults can be useful in the context of risk assessment of co-operatinginsurance companies.

Ruin probability for the quota share model with~phase-type distributed claims