Open Access
August, 1993 On Ladder Height Distributions of General Risk Processes
Masakiyo Miyazawa, Volker Schmidt
Ann. Appl. Probab. 3(3): 763-776 (August, 1993). DOI: 10.1214/aoap/1177005362

Abstract

We consider a continuous-time risk process {Ya(t);t0} defined for a stationary marked point process {(Tn,Xn)}, where Ya(0)=a and Ya(t) increases linearly with a rate c and has a downward jump at time Tn with jump size Xn for n{1,2,}. For a=0, we prove that, under a balance condition, the descending ladder height distribution of {Y0(t)} has the same form as the case where {(Tn,Xn)} is a compound Poisson process. This generalizes the recent result of Frenz and Schmidt, in which the independence of {Tn} and {Xn} is assumed. In our proof, a differential equation is derived concerning the deficit Za at the ruin time of the risk process {Ya(t)} for an arbitrary a0. It is shown that this differential equation is also useful for proving a continuity property of ladder height distributions.

Citation

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Masakiyo Miyazawa. Volker Schmidt. "On Ladder Height Distributions of General Risk Processes." Ann. Appl. Probab. 3 (3) 763 - 776, August, 1993. https://doi.org/10.1214/aoap/1177005362

Information

Published: August, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0780.60099
MathSciNet: MR1233624
Digital Object Identifier: 10.1214/aoap/1177005362

Subjects:
Primary: 60K30
Secondary: 60G10 , 90B99

Keywords: inversion formula , Palm distribution , Risk theory , ruin probability , severity of ruin , single-server queue , stationary marked point process

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.3 • No. 3 • August, 1993
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