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The dissertation addresses the topics of hospitalization insurance and long-term care insurance, with a special focus on old people. As these covers are lifelong in Belgian law, forthcoming challenges, together with inflation, are notably related to the uncertainty around population aging and the increasing life expectancy. An adequate management of longevity, morbidity and inflation risks requires insurance companies to model and measure them. Until recent years, both mortality and morbidity have been traditionally modeled in a deterministic framework. The aim of this dissertation is to analyze and disentangle health insurance related risks and their interactions and propose risk management strategies. Stochastic models are introduced to better capture the health expenditures evolution and their frequency and severity components. We introduce longevity dynamics in the models, allowing to link morbidity to mortality projections. We show that longevity and medical inflation effects can be disentangled with the help of an appropriate frequency-severity decomposition. In the last part, a “life-care tontine” design is proposed and highlights the interest of pooling mortality and morbidity risks, exploiting the correlation structure of the risks., (SC - Sciences) -- UCL, 2021

This paper offers a systematic treatment of risk-sharing rules for insurance losses, based on a list of relevant properties. A number of candidate risk-sharing rules are considered, including the conditional mean risk-sharing rule proposed in Denuit and Dhaene (2012) and the newly introduced quantile risk-sharing rule. Their compliance with the proposed properties is established. Then, methods for building new risk-sharing rules are discussed. The results derived in this paper are shown to be helpful in the development of peer-to-peer insurance (or crowdsurance), as well as to manage contingent risk funds where a given budget is distributed among claimants.

tThe Belgian Law of 20 July 2007 has drastically changed the Belgian private health insurance sector bymaking individual contracts lifelong with the technical basis (i.e. actuarial assumptions) fixed at policyissue. The goal of the Law is to ensure the accessibility to supplementary health coverage in order toprotect policyholders from discrimination and exclusion, essentially when these operate on the basis ofage. Due to the unpredictable nature of medical inflation risk and the difficulty to model future increasesof health claims, the legislator introduced medical indices together with a specific updating mechanism,which aim at establishing standardized and fair premium adjustments across the sector. This paperconsiders two major issues of the current Belgian system. The first one is related to the transferability ofthe reserves, whereas the second one is related to age-discrimination. We discuss these issues and theirinterplay, and we address the conflict between the goal of the Law and the practical problems arising inthe light of the actuarial techniques.

This paper addresses systematic longevity risk in long-term insurance business. We analyze the consequences of working under unknown survival probabilities on the efficiency of the Law of Large Numbers and point out the need for appropriate and feasible risk management techniques. We propose a setting for risk sharing schemes between the insurer and policyholders via a dynamic equivalence principle. We focus on a pure endowment contract and derive conditions for a viable risk sharing scheme which enhances the solvency situation of the insurer while being more favorably priced for the policyholders.

This paper proposes a practical way for indexing level premiums in lifelong medical insurance contracts, in order to take into account observed medical inflation. The indexing can be achieved by considering only premiums, without explicit reference to reserves. This appears to be relevant in practice as reserving mechanisms may not be transparent to policyholders and as some mutual and shareholder insurers do not compute contract-specific reserves, managing the whole portfolio in a collective way. Note that the similarity with the existing literature on life insurance comes from the lifelong nature of the contracts considered in our setting. However, in the case of health insurance covers the value of future benefits is random. The present study originates from a proposal for indexing lifelong medical insurance level premiums in Belgium. As an application, we study the impact of various indexing mechanisms on a typical medical insurance portfolio on the Belgian market.

This paper considers the problem of a lifelong health insurance cover where medical inflation is not sufficiently incorporated in the level premium determined at policy issue. We focus on the setting where changes in health benefits, driven by medical inflation, are accounted for by an appropriate update or indexation of the level premium, the policy value, or both premium and policy value, during the term of the contract. Such an updating mechanism is necessary to restore the actuarial equivalence between future health benefits and surrender values on the one hand, and available policy values and future premiums on the other hand. We extend existing literature (Vercruysse et al., 2013; Denuit et al., 2017) by developing updating mechanisms in a discrete-time framework, where medical inflation is only taken into account ex-post as it emerges over time and where surrender values are allowed for. We propose and design two types of surrender values: based on the ageing provision on the one hand and based directly on the premiums paid until surrender on the other hand. We illustrate our updating strategy with numerical examples, using Belgian data, and investigate the sensitivity of our findings with respect to elements from the technical basis (in particular: the lapse rates) used in the actuarial calculations. Our updating mechanism is generic and useful for a wide range of products in life and health insurance, where some elements of the technical basis are guaranteed while others are subject to revision according to policy conditions.

info:eu-repo/semantics/published