Ruin probability and joint distributions of some actuarial random vectors in the compound pascal model |
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| Authors: | Xian-min Geng Shu-chen Wan |
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| Institution: | (1) Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA;(2) Department of Mathematics, University of Louisville, 328 Natural Sciences Building, Louisville, KY 40292, USA;(3) Department of Mathematics, California State University Stanislaus, One University Circle, Turlock, CA 95382, USA |
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| Abstract: | The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties
of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model.
By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of
the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U(T − 1), |U(T)| and $
\mathop {\inf }\limits_{0 \leqslant n < \tau _1 }
$
\mathop {\inf }\limits_{0 \leqslant n < \tau _1 }
U(n) (i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery)
and the distributions of some actuarial random vectors. |
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| Keywords: | Compound negative binomial model Ruin probability Sequence of up-crossing zero points Ultimately leaving deficit time Joint distributions |
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