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November 2002 On Cramér-like asymptotics for risk processes with stochastic return on investments
Jostein Paulsen
Ann. Appl. Probab. 12(4): 1247-1260 (November 2002). DOI: 10.1214/aoap/1037125862

Abstract

We consider a classical risk process compounded by another independent process. Both of these component processes are assumed to be Lévy processes. We show asymptotically that as initial capital $y$ increases the ruin probability will essentially behave as $y^{-\kappa}$, where $\kappa$ depends on one of the component processes.

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Jostein Paulsen. "On Cramér-like asymptotics for risk processes with stochastic return on investments." Ann. Appl. Probab. 12 (4) 1247 - 1260, November 2002. https://doi.org/10.1214/aoap/1037125862

Information

Published: November 2002
First available in Project Euclid: 12 November 2002

zbMATH: 1019.60041
MathSciNet: MR1936592
Digital Object Identifier: 10.1214/aoap/1037125862

Subjects:
Primary: 60G99 , 90A46
Secondary: 60J27 , 60J30

Keywords: $L_p$-transform , Lévy process , Risk theory , ruin probability , stochastic difference equation

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.12 • No. 4 • November 2002
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