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Functional Large Deviations and Moderate Deviations for Markov-Modulated Risk Models with Reinsurance

Part of: Markov processes Limit theorems Mathematical economics Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Fuqing Gao  and
Jun Yan
Fuqing Gao*
Affiliation:
Wuhan University
Jun Yan*
Affiliation:
Wuhan University
*
∗Postal address: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China.
∗Postal address: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China.
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Abstract

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We establish a functional large deviation principle and a functional moderate deviation principle for Markov-modulated risk models with reinsurance by constructing an exponential martingale approach. Lundberg's estimate of the ruin time is also presented.

Keywords

Markov-modulated risk modellarge deviationsmoderate deviationsLundberg's estimate

MSC classification

Secondary: 60F10: Large deviations 60G55: Point processes 60J27: Continuous-time Markov processes on discrete state spaces 91B30: Risk theory, insurance
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 800 - 817
Copyright
Copyright © Applied Probability Trust 2008 

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