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Common Poisson Shock Models: Applications to insurance and credit risk modelling

by Filip Lindskog of Risklab and ETH Zentrum, and
Alexander J. McNeil of ETH Zentrum

November 2003

Abstract: The idea of using common Poisson shock processes to model dependent event frequencies is well known in the reliability literature. In this paper we examine these models in the context of insurance loss modelling and credit risk modelling. To do this we set up a very general common shock framework for losses of a number of different types that allows for both dependence in loss frequencies across types and dependence in loss severities. Our aims are threefold: to demonstrate that the common shock model is a very natural way of approaching the modelling of dependent losses in an insurance or risk management context; to provide a number of analytical results concerning the nature of the dependence implied by the common shock specification; to examine the aggregate loss distribution that results from the model and the sensitivity of its tail to the specification of the model parameters.

Published in: ASTIN Bulletin, Vol. 33, No. 2, (November 2003), pp. 209-238.

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