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.

Stochastic Bounds for the Sparre Andersen Process

ZUCCA, CRISTINA
2005

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.
7 (2)
225
247
Risk reserve processes; Sparre Andersen process; usual stochastic order; convex order; positive dependence; bounds; risk processes perturbed by diffusion; ruin probabilities within finite time.
F. Pellerey; C. Zucca
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/10755
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