Antisélection et demande d'assurance : Modélisation de la demande d'assurance en fonction du niveau de prime et du profil de risque de l'assuré

Details

Supervisors

Denuit, Michel

Faculty

Faculté des sciences

Degree label

Master [120] en sciences actuarielles, à finalité spécialisée

Abstract

enAdverse selection constitutes a structural challenge in insurance markets. When an insurer applies a uniform premium to individuals with heterogeneous risk profiles, it creates the conditions for an imbalance: low-risk individuals progressively withdraw from the market, while high-risk individuals remain overrepresented. This thesis analyses this mechanism through the modelling of insurance demand as a function of the premium level and the risk profile of the policyholder. First, the economic foundations of insurance demand are presented through the expected utility theory of Von Neumann and Morgenstern (1947) and the concept of risk aversion. It is shown that in the presence of an actuarially fair premium, a risk-averse individual chooses full coverage, while the existence of a loading leads to partial coverage. Second, the phenomenon of adverse selection is analysed through the seminal models of Akerlof (1970) and Rothschild and Stiglitz (1976). It is shown that information asymmetry between the insurer and policyholders leads to an overrepresentation of the highest-risk individuals in the portfolio, resulting in an increase in the average claims cost and a progressive withdrawal of low-risk individuals from the market. Third, three proportional demand functions are modelled and analysed: the iso-elastic demand function, the negative exponential demand function and the demand function of De Jong and Ferris (2006). Numerical illustrations carried out with two risk groups show that, regardless of the demand function considered, an increase in the sensitivity of demand to the premium favours the exit of low-risk individuals, raises the equilibrium premium and worsens adverse selection. Furthermore, the results show that premium pooling improves loss coverage relative to risk-differentiated pricing only under certain conditions, particularly when demand elasticity remains sufficiently low.