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RATIO MONOTONICITY FOR TAIL PROBABILITIES IN THE RENEWAL RISK MODEL

Published online by Cambridge University Press:  31 March 2011

Georgios Psarrakos  and
Michael Tsatsomeros
Georgios Psarrakos
Affiliation:
Department of Statistics and Insurance Science, University of Piraeus, Piraeus 18534, Greece E-mail: [email protected]
Michael Tsatsomeros
Affiliation:
Department of Mathematics, Washington State University, Pullman, WA 99164-3113, E-mail: [email protected]
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Abstract

A renewal model in risk theory is considered, where is the tail of the distribution of the deficit at ruin with initial surplus u and is the tail of the ladder height distribution. Conditions are derived under which the ratio is nondecreasing in u for any y≥0. In particular, it is proven that if the ladder height distribution is stable and DFR or phase type, then the above ratio is nondecreasing in u. As a byproduct of this monotonicity, an upper bound and an asymptotic result for are derived. Examples are given to illustrate the monotonicity results.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 2 , April 2011 , pp. 171 - 185
Copyright
Copyright © Cambridge University Press 2011

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