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

Dimitrova, D. S., Ignatov, Z. G. & Kaishev, V. K. (2017). On the First Crossing of Two Boundaries by an Order Statistics Risk Process. Risks, 5(3), 43. doi: 10.3390/risks5030043

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.

Publication Type:	Article
Publisher Keywords:	double boundary non-crossing probability; point process; risk process; ruin probability; Appell polynomials
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management
Departments:	Bayes Business School > Actuarial Science & Insurance