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Ruin probabilities in a diffusion environment

Part of: Special processes Markov processes Limit theorems Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Jan Grandell  and
Hanspeter Schmidli
Jan Grandell
Affiliation:
Royal Institute of Technology, Department of Mathematics, Royal Institute of Technology, SE-10044 Stockholm, Sweden
Hanspeter Schmidli
Affiliation:
University of Cologne, Department of Mathematics, University of Cologne, Weyertal 86-90, D-50931 Cologne, Germany. Email address: schmidli@math.uni-koeln.de
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Abstract

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We consider an insurance model, where the underlying point process is a Cox process. Using a martingale approach applied to diffusion processes, finite-time Lundberg inequalities are obtained. By change-of-measure techniques, Cramér–Lundberg approximations are derived.

Keywords

Ruin probabilityLundberg inequalityCox processdiffusion processmartingale methodchange-of-measure technique

MSC classification

Primary: 60K37: Processes in random environments 60J60: Diffusion processes
Secondary: 60G44: Martingales with continuous parameter 60F10: Large deviations
Type
Part 1. Risk Theory
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 39 - 50
Copyright
Copyright © Applied Probability Trust 2011 

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