Reserving for health and general insurance contracts. Essays on transferability mechanisms and micro-level techniques.

SCIENTIFIC SUMMARY (English)

The research in this PhD dissertation contributes to the non-life insurance reserving literature.  We focus on two specific research questions: (1) the development of the actuarial techniques to appropriately handle the unpredictable medical inflation in context of private health insurance contracts with transferable reserves and (2) the development of micro-level claims reserving techniques that provide an alternative for the existing aggregated methods.

Lifelong health insurance contracts

Chapter 2 of the dissertation is entitled 'Updating mechanisms for lifelong health insurance contracts with reserve- or premium-based surrender values'.  For lifelong health insurance covers, medical inflation not sufficiently incorporated in the level premiums determined at policy issue requires an appropriate increase of these premiums, the corresponding reserves or both during the term of the contract.  Such a premium or reserve update is necessary to maintain the actuarial equivalence between future health benefits and surrender values on the one hand, and available reserves and future premiums on the other hand. In Vercruysse et al. (2013) and Denuit et al. (2015), premium and reserve indexing mechanisms were proposed in a discrete-time framework where medical inflation is only taken into account ex-post as it emerges over time and where the reserves are not transferable in case of policy cancellation. In this chapter, we extend this work by investigating the more general situation where a surrender value is paid out in case of policy cancellation. Reserve-based as well as premium-based surrender values are considered.

Micro-level claims reserving

Insurance companies hold reserves to be able to fulfill future liabilities with respect to the policies they write.  Micro-level reserving methods focus on the development of individual claims over time, providing an alternative to the classical techniques that aggregate the development of claims into run-off triangles. 

Chapter 3, 'Reserving by conditioning on markers of individual claims - A case study using historical simulation', explores the use of claim specific characteristics, so-called claim markers, for loss reserving with individual claims. Starting from the approach of Rosenlund (2012) and using the technique of historical simulation we develop a stochastic Reserve by Detailed Conditioning (`RDC') method which is applicable to a micro-level data set with detailed information on individual claims.  We construct the predictive distribution of the outstanding loss reserve by simulating future payments of a claim, given its claim markers.  We demonstrate the performance of the method on a portfolio of general liability insurance policies for private individuals from a European insurance company. Hereby we explore how to incorporate different kinds of claim markers and evaluate the impact of the set of markers and their specification on the predictive distribution of the outstanding reserve.

Chapter 4 of the PhD dissertation is entitled 'A multi-state approach and flexible payment distributions for micro-level reserving in general insurance'.   This chapter presents a discrete-time multi-state framework that reconstructs the claim development process as a series of transitions between a given set of states.  The states in our setting represent the events that may happen over the lifetime of a claim, i.e.~reporting, intermediate payments and closure.  For each intermediate payment we model the payment distribution separately.  To this end, we use a body-tail approach where the body of the distribution is modeled separately from the tail.  Generalized Additive Models for Location, Scale and Shape introduced by Stasinopoulos & Rigby (2007) allow for flexible modeling of the body distribution while incorporating covariate information.  We use the toolbox from Extreme Value Theory to determine the threshold separating the body from the tail and to model the tail of the payment distributions.  We do not correct payments for inflation beforehand, but include relevant covariate information in the model.  Using these building blocks, we outline a simulation procedure to evaluate the RBNS reserve.  The method is applied to a real life data set, and we benchmark our results by means of a back test.