Modèles de renouvellement avec effets de tendance, et application à l'assurance pour fautes des professionnels de la santé
|Abstract:||In this thesis, we present a very large class of counting processes including the renewal process and the non-homogeneous Poisson process, to which we add stochastic discount rates, in order to model the aggregate cost related to medical malpractice insurance. In the introduction, we present some important characteristics related to the cost process of medical malpractice insurance. In Chapter 1, we present some theoretical concepts that will be used to build the aggregate cost process related to the medical malpractice insurance model that is proposed in Chapter 4. In Chapter 2, we present some results related to the compound non-homogeneous Poisson and compound Cox processes with a discount factor. In particular, we derive an analytic expression for the moment generating functions that will be inverted numerically using Fourier transforms in order to obtain an approximation of the probability distribution function. In Chapter 3, we study a class of models that generalizes the class of models studied in Chapter 2 : the compound trend renewal process with discount factor. For this new class of processes, we obtain recursive formulas for the moment calculations and an analytic expression for the moment generating function. The moment generating function can be inverted analytically or numerically for many particular cases in order to obtain an exact expression or an approximation of the probability distribution function. In Chapter 4, we present the stochastic model that will be used to measure the risk of an agregate cost related to medical malpractice insurance, which also generalizes the class of models considered in Chapter 3. In Chapter 5, we calibrate the model proposed in Chapter 4 on the closed claims database of Florida. The conclusion follows with a short summary of the results and an outline of some extensions for future research.|
|Document Type:||Thèse de doctorat|
|Open Access Date:||22 December 2018|
|Collection:||Thèses et mémoires|
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