The goal of this study was to model the behaviour of supplementary health insurance policyholders within a context of moral hazard and build an optimal contract resolution algorithm. The optimal contract maximizes the insurer’s expected   profit under participation and incentive constraints: the insured remains in such a contract and chooses the effort to limit risk exposure that maximizes its expected utility. Moral hazard is a situation of information asymmetry where the insurer cannot observe the effort but only an imperfect signal from it, called “output”. The expected utility of the insured is here the difference between the expected utility of wealth and the cost of the effort.
We developed a theoretical framework based on the Contract Theory for health insurance. Using French supplementary health insurance data, we constructed effort indicators to model the insured’s behaviour (frequency and intensity of use of cover) for each risk class. The algorithm calibrates the moral hazard model, in particular the utility of wealth, according to the degree of risk-aversion and the cost of effort according to the participation and incentive conditions of the initial contract. Finally, the numerical resolution of the model identifies the characteristics of the optimal contract (premium, deductible, and coverage ceiling) as well as the insured’s behaviour (effort).
 The algorithm provides an innovative approach to insurance companies wishing to develop competitive and sustainable insurance products.