arXiv subjects

Jonas Crevecoeur

Publications and source records attributed to Jonas Crevecoeur.

4 recordsLinked to original sources

arXiv2023

Bridging the gap between pricing and reserving with an occurrence and development model for non-life insurance claims

Due to the presence of reporting and settlement delay, claim data sets collected by non-life insurance companies are typically incomplete, facing right censored claim count and claim severity observations. Current practice in non-life insurance pricing tackles these right censored data via a two-step procedure. First, best estimates are computed for the number of claims that occurred in past exposure periods and the ultimate claim severities, using the incomplete, historical claim data. Second, pricing actuaries build predictive models to estimate technical, pure premiums for new contracts by treating these best estimates as actual observed outcomes, hereby neglecting their inherent uncertainty. We propose an alternative approach that brings valuable insights for both non-life pricing as well as reserving. As such we effectively bridge these two key actuarial tasks that have traditionally been discussed in silos. Hereto we develop a granular occurrence and development model for non-life claims that tackles reserving and at the same time resolves the inconsistency in traditional pricing techniques between actual observations and imputed best estimates. We illustrate our proposed model on an insurance as well as a reinsurance portfolio. The advantages of our proposed strategy are most compelling in the reinsurance illustration where large uncertainties in the best estimates originate from long reporting and settlement delays, low claim frequencies and heavy (even extreme) claim sizes.

q-fin.RM↗

arXiv2021

A hierarchical reserving model for reported non-life insurance claims

Traditional non-life reserving models largely neglect the vast amount of information collected over the lifetime of a claim. This information includes covariates describing the policy, claim cause as well as the detailed history collected during a claim's development over time. We present the hierarchical reserving model as a modular framework for integrating a claim's history and claim-specific covariates into the development process. Hierarchical reserving models decompose the joint likelihood of the development process over time. Moreover, they are tailored to the portfolio at hand by adding a layer to the model for each of the events registered during the development of a claim (e.g. settlement, payment). Layers are modelled with statistical learning (e.g. generalized linear models) or machine learning methods (e.g. gradient boosting machines) and use claim-specific covariates. As a result of its flexibility, this framework incorporates many existing reserving models, ranging from aggregate models designed for run-off triangles to individual models using claim-specific covariates. This connection allows us to develop a data-driven strategy for choosing between aggregate and individual reserving; an important decision for reserving practitioners. We illustrate our method with a case study on a real insurance data set and deduce new insights in the covariates driving the development of claims. Moreover, we evaluate the method's performance on a large number of simulated portfolios representing several realistic development scenarios and demonstrate the flexibility and robustness of the hierarchical reserving model.

q-fin.RM↗

arXiv2021

Modeling the occurrence of events subject to a reporting delay via an EM algorithm

A delay between the occurrence and the reporting of events often has practical implications such as for the amount of capital to hold for insurance companies, or for taking preventive actions in case of infectious diseases. The accurate estimation of the number of incurred but not (yet) reported events forms an essential part of properly dealing with this phenomenon. We review the current practice for analysing such data and we present a flexible regression framework to jointly estimate the occurrence and reporting of events. By linking this setting to an incomplete data problem, estimation is performed via an expectation-maximization algorithm. The resulting method is elegant, easy to understand and implement, and provides refined insights in the nowcasts. The proposed methodology is applied to a European general liability portfolio in insurance.

stat.AP↗

arXiv2019

Modeling the number of hidden events subject to observation delay

This paper considers the problem of predicting the number of events that have occurred in the past, but which are not yet observed due to a delay. Such delayed events are relevant in predicting the future cost of warranties, pricing maintenance contracts, determining the number of unreported claims in insurance and in modeling the outbreak of diseases. Disregarding these unobserved events results in a systematic underestimation of the event occurrence process. Our approach puts emphasis on modeling the time between the occurrence and observation of the event, the so-called observation delay. We propose a granular model for the heterogeneity in this observation delay based on the occurrence day of the event and on calendar day effects in the observation process, such as weekday and holiday effects. We illustrate this approach on a European general liability insurance data set where the occurrence of an accident is reported to the insurer with delay.

q-fin.RM↗