Panel Count Data with Dynamic Random Effects in Actuarial Sciences

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My research program is about mathematical developments for general insurance (Fire, Accident & Casualty). The main idea is to model the number of claims to an insurer where the dependence between all the contracts of the same insured, called panel data structure, will be put forward in the modeling. To do this, the research program is divided into two independent axes: 1. A theoretical approach that requires new statistical developments on time series for count, before the preliminary application to real data panel. Various forms of conditional distributions (such as hurdle or zero-inflated models) will be tested, and various forms of the underlying dynamic process will also be verified (generalization of the multifractal models with a larger number of fractal processes, or using other forms of processes). New estimation techniques and new time series models will be used and generalized, such as filtering techniques, like particle filter approximation or a linear Kalman filter, for example. Because of their high speed, multifractal models can also be used in some importance sampling methods. 2. A practical approach based on bonus-malus systems (BMS) where, instead of working with an advanced statistical model that creates time dependence between all the contracts of the same insured, we assume that a BMS plays this role. In this innovative approach, a new criterion is proposed based on a competitive angle. Indeed, the insurer must offer a premium high enough to cover the risk, but lower than that of the competitors. We will select the best BMS on this criterion instead of using classic information criterion based on log-likelihood statistics.