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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)

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