Stochastic Bounds for the Sparre Andersen Process

Franco Pellerey () and Cristina Zucca ()
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Franco Pellerey: Politecnico di Torino
Cristina Zucca: Università degli Studi di Torino

Methodology and Computing in Applied Probability, 2005, vol. 7, issue 2, 225-247

Abstract: Abstract In this paper we define two stochastic processes that are smaller and greater in usual stochastic order than the Sparre Andersen process. We derive, as a consequence, upper and lower bounds of its marginal distributions, and of the distributions of its first passage times above fixed thresholds. We also present a generalization of these stochastic bounds for risk processes perturbed by diffusion.

Keywords: risk reserve processes; Sparre Andersen process; usual stochastic order; convex order; positive dependence; bounds; risk processes perturbed by diffusion; ruin probabilities within finite time (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s11009-005-1484-0

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