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The joint distribution of surplus immediately before ruin and the deficit at ruin under interest force. (English) Zbl 1083.62547
Summary: We consider a compound Poisson risk model with a constant interest force. We investigate the joint distribution of the surplus immediately before and after ruin. By adapting the techniques of B. Sundt and J. L. Teugels [Insur. Math. Econ. 16, 7–22 (1995; Zbl 0838.62098)], we obtain integral equations satisfied by the joint distribution function and a Lundberg-type inequality. In the case of zero initial reserve and the case of exponential claim sizes, we obtain explicit expressions for the joint distribution function.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
62E15 Exact distribution theory in statistics
91B30 Risk theory, insurance (MSC2010)
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