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Ruin estimation for a general insurance risk model. (English) Zbl 0811.62096
An insurance risk model is introduced and studied where borrowing is allowed with interest rate \(\beta_ 2\) and interest is obtained for capital above a certain level (the liquid reserve) with rate \(\beta_ 1\). Also an inflation rate can be considered. Martingales of the form \(\{f(X_ t)\}\) are constructed by use of the theory of piecewise- deterministic Markov processes \(\{X_ t\}\) where \(\{X_ t\}\) is here the surplus process. Then the ruin probability can be given in terms of \(f\). However, \(f\) is defined only through its Laplace transform unless the claim-size distribution is exponential. It is indicated how \(f\) can be approximated by numerical procedures. The behaviour of ruin probability for large initial capital is described by the Lundberg exponent.
Reviewer: M.Schäl (Bonn)

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
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