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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.

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