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On the First Crossing of Two Boundaries by an Order Statistics Risk Process

Dimitrina S. Dimitrova (), Zvetan G. Ignatov () and Vladimir K. Kaishev ()
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Dimitrina S. Dimitrova: Faculty of Actuarial Science and Insurance, Cass Business School, City, University of London, 106 Bunhill Row, London EC1Y 8TZ, UK
Zvetan G. Ignatov: Faculty of Economics and Business Administration, Sofia University “St Kliment Ohridski”, 125 Tsarigradsko Shosse Blv., bl.3, Sofia 1113, Bulgaria
Vladimir K. Kaishev: Faculty of Actuarial Science and Insurance, Cass Business School, City, University of London, 106 Bunhill Row, London EC1Y 8TZ, UK

Risks, 2017, vol. 5, issue 3, 1-14

Abstract: We derive a closed form expression for the probability that a non-decreasing, pure jump stochastic risk process with the order statistics (OS) property will not exit the strip between two non-decreasing, possibly discontinuous, time-dependent boundaries, within a finite time interval. The result yields new expressions for the ruin probability in the insurance and the dual risk models with dependence between the claim severities or capital gains respectively.

Keywords: double boundary non-crossing probability; point process; risk process; ruin probability; Appell polynomials (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 M2 M4 K2 (search for similar items in EconPapers)
Date: 2017
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