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International audience

International audience

International audience

This paper presents a model for the determination and forecast of the number of defaults and credit changes by estimating a reduced-form ordered regression model with a large data set from a credit insurance portfolio. Similarly to banks with their classical credit risk management techniques, credit insurers measure the credit quality of buyers with rating transition matrices depending on the economical environment. Our approach consists in modeling stochastic transition matrices for homogeneous groups of firms depending on macroeconomic risk factors. One of the main features of this business is the close monitoring of covered firms and the insurer’s ability to cancel or reduce guarantees when the risk changes. As our primary goal is a risk management analysis, we try to account for this leeway and study how this helps mitigate risks in case of shocks. This specification is particularly useful as an input for the Own Risk Solvency Assessment (ORSA) since it illustrates the kind of management actions that can be implemented by an insurer when the credit environment is stressed.

International audience

Studying Long Term Care (LTC) insurance requires modeling the lifetime of individuals in presence of both terminal and non-terminal events which are concurrent. Although a non-homogeneous semi-Markov multi-state model is probably the best candidate for this purpose, most of the current researches assume, maybe abusively, that the Markov assumption is satisfied when fitting the model. In this context, using the Aalen–Johansen estimators for transition probabilities can induce bias, which can be important when the Markov assumption is strongly unstated. Based on some recent studies developing non-Markov estimators in the illness–death model that we can easily extend to a more general acyclic multi-state model, we exhibit three non-parametric estimators of transition probabilities of paying cash-flows, which are of interest when pricing or reserving LTC guarantees in discrete time. As our method directly estimates these quantities instead of transition intensities, it is possible to derive asymptotic results for these probabilities under non-dependent random right-censorship, obtained by re-setting the system with two competing risk blocks. Inclusion of left-truncation is also considered. We conduct simulations to compare the performance of our transition probabilities estimators without the Markov assumption. Finally, we propose a numerical application with LTC insurance data, which is traditionally analyzed with a semi-Markov model.