Dottorato in SCUOLA DI SCIENZE STATISTICHE

Titolo della tesi: Claim probability in Credit and Suretyship insurance

This work analyses the problems faced by a Credit and Suretyship (C&S) insurance company when inferring claim probabilities and proposes a set of dedicated tools to address these problems. Typically, a small amount of information is available to calibrate the C&S claim probability. C&S insurers observe a low claim frequency on average and, in credit insurance, are subject to a remarkable information asymmetry concerning their insured sellers. Further, they cannot enjoy the typical information facilities available for the banks that share information regarding their risk sources through centralized databases. These elements imply the need to perform a precise calibration of claim probabilities (both marginal and joint probabilities) based on data sets that are often scarcely populated. In the first part of the thesis, the central contracts offered by this insurance line of business are outlined regarding both credit insurance products and suretyship bonds. The contractual analysis aims to highlight to what extent the claims generated by the two sub-lines (Credit insurance and suretyship) can be legitimately modeled under the same framework. After identifying the main features shared among all the C&S contracts, a selection of classical credit risk models is considered to decide which best fits the modeling requirements for representing a C&S claim. The CreditRisk+ model turns out to cope with all the identified C&S claim features; thus, it is chosen to describe the dependence structure among future claim events. Concerning the estimation of marginal claim probabilities, the analysis is based on the fact that all the C&S claims are absorbing events and that - in credit insurance - the presence of censoring events must be taken into account. A selection of classical methods to estimate the real-world probability of absorbing events, either in the presence of censoring events or not, is compared against the specific features of the claims to be modeled. The classical estimator of the Bernoulli distribution’s parameter proves adequate to quantify the marginal claim probability for a suretyship risk. On the other hand, even the Kaplan-Meyer and Cutler-Ederer estimators are not adequate to model the credit insurance claim probability properly, despite being designed to handle the effects of censoring events. Given the vast lack of results developed explicitly for the C&S claim probability topic, many actuarial problems worth attention are yet to be investigated. In the second part of this work, we address three specific research problems encountered in the first part without claim to completeness. We propose a technique to calibrate the CreditRisk+ dependence structure parameters with particular reference to the cases when only a small data set is available, as is often the case in C&S insurance. The calibration is achieved by generalizing the model to a multi-period framework. With specific regard to suretyship insurance, we investigated the phenomenon of bid bond claims generated by the insurers themselves when they refuse to issue a performance bond to the winner of a public tender. This particular case turns out to be mainly originated by a poor choice of the starting price in the tender process. We propose a risk appetite framework specifically designed to prevent this type of claim. Finally, we propose a new parametric frequency estimator to address the problem of estimating claim probability in credit insurance, given the information asymmetry between the insurer and the insured and the related censoring events. The concluding remarks provide insight on some research lines worth to be considered and that this work leaves open.