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.

Predictive modeling uses data to forecast future events. It exploits relationships between explanatory variables and the predicted variables from past occurrences to predict future outcomes. Forecasting financial events is a core skill that actuaries routinely apply in insurance and other risk-management applications. Predictive Modeling Applications in Actuarial Science emphasizes life-long learning by developing tools in an insurance context, providing the relevant actuarial applications, and introducing advanced statistical techniques that can be used to gain a competitive advantage in situations with complex data. Volume 2 examines applications of predictive modeling. Where Volume 1 developed the foundations of predictive modeling, Volume 2 explores practical uses for techniques, focusing on property and casualty insurance. Readers are exposed to a variety of techniques in concrete, real-life contexts that demonstrate their value and the overall value of predictive modeling, for seasoned practicing analysts as well as those just starting out.

Focusing on life insurance and pensions, this book addresses various aspects of modelling in modern insurance: insurance liabilities; asset-liability management; securitization, hedging, and investment strategies. With contributions from internationally renowned academics in actuarial science, finance, and management science and key people in major life insurance and reinsurance companies, there is expert coverage of a wide range of topics, for example: models in life insurance and their roles in decision making; an account of the contemporary history of insurance and life insurance mathematics; choice, calibration, and evaluation of models; documentation and quality checks of data; new insurance regulations and accounting rules; cash flow projection models; economic scenario generators; model uncertainty and model risk; model-based decision-making at line management level; models and behaviour of stakeholders. With author profiles ranging from highly specialized model builders to decision makers at chief executive level, this book should prove a useful resource to students and academics of actuarial science as well as practitioners.

Predictive modeling involves the use of data to forecast future events. It relies on capturing relationships between explanatory variables and the predicted variables from past occurrences and exploiting this to predict future outcomes. Forecasting future financial events is a core actuarial skill - actuaries routinely apply predictive-modeling techniques in insurance and other risk-management applications. This book is for actuaries and other financial analysts who are developing their expertise in statistics and wish to become familiar with concrete examples of predictive modeling. The book also addresses the needs of more seasoned practising analysts who would like an overview of advanced statistical topics that are particularly relevant in actuarial practice. Predictive Modeling Applications in Actuarial Science emphasizes lifelong learning by developing tools in an insurance context, providing the relevant actuarial applications, and introducing advanced statistical techniques that can be used by analysts to gain a competitive advantage in situations with complex data.

The book provides a sound mathematical base for life insurance mathematics and applies the underlying concepts to concrete examples. Moreover the models presented make it possible to model life insurance policies by means of Markov chains. Two chapters covering ALM and abstract valuation concepts on the background of Solvency II complete this volume. Numerous examples and a parallel treatment of discrete and continuous approaches help the reader to implement the theory directly in practice.

Predictive modeling uses data to forecast future events. It exploits relationships between explanatory variables and the predicted variables from past occurrences to predict future outcomes. Forecasting financial events is a core skill that actuaries routinely apply in insurance and other risk-management applications. Predictive Modeling Applications in Actuarial Science emphasizes life-long learning by developing tools in an insurance context, providing the relevant actuarial applications, and introducing advanced statistical techniques that can be used to gain a competitive advantage in situations with complex data. Volume 2 examines applications of predictive modeling. Where Volume 1 developed the foundations of predictive modeling, Volume 2 explores practical uses for techniques, focusing on property and casualty insurance. Readers are exposed to a variety of techniques in concrete, real-life contexts that demonstrate their value and the overall value of predictive modeling, for seasoned practicing analysts as well as those just starting out.

This book summarizes the state of the art in generalized linear models (GLMs) and their various extensions: GAMs, mixed models and credibility, and some nonlinear variants (GNMs). In order to deal with tail events, analytical tools from Extreme Value Theory are presented. Going beyond mean modeling, it considers volatility modeling (double GLMs) and the general modeling of location, scale and shape parameters (GAMLSS). Actuaries need these advanced analytical tools to turn the massive data sets now at their disposal into opportunities. The exposition alternates between methodological aspects and case studies, providing numerical illustrations using the R statistical software. The technical prerequisites are kept at a reasonable level in order to reach a broad readership. This is the first of three volumes entitled Effective Statistical Learning Methods for Actuaries. Written by actuaries for actuaries, this series offers a comprehensive overview of insurance data analytics with applications to P&C, life and health insurance. Although closely related to the other two volumes, this volume can be read independently.