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Application of advanced statistical analysis for internal modeling in life insurance

Abstract : The Basel agreements and the associated European directives have made banking prudential capital contingent on their risk profile rather than on their size or turnover. The Solvency 2 Directive (hereinafter the "Directive") repeats this process for European insurers and reinsurers. It constitutes a total paradigm shift for the majority of European insurers. It defines the main regulatory principles aimed at regulating their activity and in particular determining the amount of prudential capital associated with the risks inherent to their activity.In accordance with the directive, the prudential capital corresponds in principle to an insurer with a 99.5% percentile of the change in its basic own funds over the coming year. Such a prospective risk measure requires for an insurer the ability to address two problems: a valuation problem and a simulation problem. In practice, the 99.5% percentile of the change in basic own funds is estimated using the MonteCarlo method. It is particularly sensitive to the one-year law retained for the risk factors vector. Its Monte Carlo valuation would ideally require the simulation of one year risk factor vector x and the valuation of the associated equity values. Given the significant calculation time required for numerical evaluation, this approach is in practice unsuitable. In order to circumvent this problem, the insurers have developed many approximate methods or "proxies" which make it possible to approximate the basic own funds value instantaneously. Today, these methods are rarely accompanied by error controls that would measure the simulation quality. More precisely, the methods currently used by the insurers do not make it possible to control naturally the approximation error generated by the use of the proxy model instead. The proposed error checks are therefore always empirical and too approximate.In order to solve this problematic, we propose, in a first part of this thesis, a new method of constructing the proxy that is both resource-efficient and offers rigorous error control. The second part of this thesis aims at applying the extreme value theory to the prudential capital estimate when information on the covariate is available. In particular, when the covariate is high dimensional, we are confronted with the problem of the curse of dimensionality, which translates into a decrease in the fastest possible convergence rates of estimators of the regression function to their target curve. This problem refers to the phenomenon where the volume of the covariate increases so rapidly that available data become sparse. To obtain a statistically reliable result, the amount of data needed to support the result often increases exponentially with dimensionality, which is generally problematic in many practical applications. To overcome this estimation problem, we propose a new efficient evaluation methodology by combining the generalized additive model and the sparse group lasso method.
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Submitted on : Wednesday, December 15, 2021 - 4:06:25 PM
Last modification on : Friday, August 5, 2022 - 3:00:08 PM
Long-term archiving on: : Wednesday, March 16, 2022 - 7:18:17 PM


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  • HAL Id : tel-03481989, version 1


Quang Dien Duong. Application of advanced statistical analysis for internal modeling in life insurance. General Mathematics [math.GM]. Sorbonne Université, 2021. English. ⟨NNT : 2021SORUS212⟩. ⟨tel-03481989⟩



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