Provisionnement en assurance non-vie pour des contrats à maturité longue et à prime unique : application à la réforme Solvabilité 2

Abstract : We consider an insurance company which has to indemnify a bank against losses related to a borrower defaulting on payments. Models normally used by insurers are collectives and do not allows to take into account the personal characteristics of borrowers. In a first part, we defined a model to evaluate potential future default amounts (provision) over a fixed period.The amount of default is the key to our model. For a borrower j and an associated maturity Tj, this amount is max(Sj Tj -Rj Tj ; 0), where Sj Tj is the outstanding amount owed by the borrower and depends on the borrowed amount and the term of the loan, and Rj Tj is the property sale amount. Rj Tj is proportionate to the borrowed amount; the proportionality coefficient is modeled by a geometric Brownian motion and represents the fluctuation price of real estate. The couples (Maturity of the loan, Term of the loan) are modeled by a Poisson point process. The provision Ph, where h is the maximum duration of the loans, is defined as the sum of the random number of individual defaults amounts. We can calculate the mean and the variance of the provision and also give an algorithm to simulate the provision. It is also possible to estimate the parameters of our model and then give a numerical value of the provision quantile. In the second part we will focus on the solvency need due to provisioning risk (topic imposed by the european Solvency 2 reform). The question will be to study the asymptotic behaviour of Ph when h ! +1. We will show that Ph, well renormalized, converges in law to a random variable which is the sum of two random variables whose one is a Gaussian
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Geoffrey Nichil. Provisionnement en assurance non-vie pour des contrats à maturité longue et à prime unique : application à la réforme Solvabilité 2. Mathématiques générales [math.GM]. Université de Lorraine, 2014. Français. ⟨NNT : 2014LORR0200⟩. ⟨tel-01751162⟩

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