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Risks 2017, 5(3), 43; doi:10.3390/risks5030043

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

1
Faculty of Actuarial Science and Insurance, Cass Business School, City, University of London, 106 Bunhill Row, London EC1Y 8TZ, UK
2
Faculty of Economics and Business Administration, Sofia University “St Kliment Ohridski”, 125 Tsarigradsko Shosse Blv., bl.3, Sofia 1113, Bulgaria
*
Author to whom correspondence should be addressed.
Academic Editor: Mogens Steffensen
Received: 14 July 2017 / Revised: 11 August 2017 / Accepted: 15 August 2017 / Published: 18 August 2017
View Full-Text   |   Download PDF [389 KB, uploaded 18 August 2017]

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. View Full-Text
Keywords: double boundary non-crossing probability; point process; risk process; ruin probability; Appell polynomials double boundary non-crossing probability; point process; risk process; ruin probability; Appell polynomials
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Dimitrova, D.S.; Ignatov, Z.G.; Kaishev, V.K. On the First Crossing of Two Boundaries by an Order Statistics Risk Process. Risks 2017, 5, 43.

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