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The joint distributions of several important actuarial diagnostics in the classical risk model. (English) Zbl 1071.91027
For the risk process consisting of a compound Poisson part and a constant premium flow the authors derive the distribution and joint distribution of various associated variables. These include the surplus prior to ruin, the deficit at ruin, the maximum and minimum profit before ruin etc. These are sometimes called actuarial diagnostic variables, because they provide significant information and the overall risk process. If the individual claim distribution is exponential, explicit formulae are given. In the proof essential use of the strong Markov property is made. The paper is of the bare Theorem-proof type with practically no explanation or interpretation.

91B30 Risk theory, insurance (MSC2010)
60J25 Continuous-time Markov processes on general state spaces
Full Text: DOI
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