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A transient Cramér–Lundberg model with applications to credit risk

Part of: Stochastic processes Applications

Published online by Cambridge University Press:  16 September 2021

Guusje Delsing Open the ORCID record for Guusje Delsing [Opens in a new window]  and
Michel Mandjes
Guusje Delsing*
Affiliation:
University of Amsterdam and Rabobank
Michel Mandjes*
Affiliation:
University of Amsterdam
*
*Postal address: Korteweg–de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands.
*Postal address: Korteweg–de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands.
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Abstract

This paper considers a variant of the classical Cramér–Lundberg model that is particularly appropriate in the credit context, with the distinguishing feature that it corresponds to a finite number of obligors. The focus is on computing the ruin probability, i.e. the probability that the initial reserve, increased by the interest received from the obligors and decreased by the losses due to defaults, drops below zero. As well as an exact analysis (in terms of transforms) of this ruin probability, an asymptotic analysis is performed, including an efficient importance-sampling-based simulation approach.

The base model is extended in multiple dimensions: (i) we consider a model in which there may, in addition, be losses that do not correspond to defaults, (ii) then we analyze a model in which the individual obligors are coupled via a regime switching mechanism, (iii) then we extend the model so that between the losses the reserve process behaves as a Brownian motion rather than a deterministic drift, and (iv) we finally consider a set-up with multiple groups of statistically identical obligors.

Keywords

Cramér–Lundberg processruin probabilitylarge-deviation asymptoticsimportance sampling

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 62P05: Applications to actuarial sciences and financial mathematics
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 3 , September 2021 , pp. 721 - 745
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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