Mixed exponential distributions are frequently used in actuarial risk modeling. Distributions obtained through mixtures allow greater flexibility in the modeling of non-life insurance loss amounts . Several research works have studied mixed exponential distributions in univariate and multivariate settings. The present paper highlights the usefulness of such distributions and lays the story of the mixing technique behind them. It also explains the underlying link between all these works. In addition, a comprehensive study of three special cases of mixing distributions is considered. Applications in actuarial science of these distributions are presented throughout the paper highlighting their many uses and useful properties.

Multivariate Survival Analysis and Competing Risks introduces univariate survival analysis and extends it to the multivariate case. It covers competing risks and counting processes and provides many real-world examples, exercises, and R code. The text discusses survival data, survival distributions, frailty models, parametric methods, multivariate

Much of actuarial science deals with the analysis and management of financial risk. In this text we address the topic of loss models, traditionally called risk theory by actuaries, including the estimation of such models from sample data. The theory of survival models is addressed in other texts, including the ACTEX work entitled Models for Quantifying Risk which might be considered a companion text to this one. In Risk Models and Their Estimation we consider as well the estimation of survival models, in both tabular and parametric form, from sample data. This text is a valuable reference for those preparing for Exam C of the Society of Actuaries and Exam 4 of the Casualty Actuarial Society. A separate solutions' manual with detailed solutions to the text exercises is also available.

Extreme Value Modeling and Risk Analysis: Methods and Applications presents a broad overview of statistical modeling of extreme events along with the most recent methodologies and various applications. The book brings together background material and advanced topics, eliminating the need to sort through the massive amount of literature on the subje

In actuarial science, collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of random sums, play a crucial role. In these models, it is common to assume that the number of claims and their amounts are independent, even if this might not always be the case. We consider collective risk models with different dependence structures. Due to the importance of such distributions in an actuarial setting, we first investigate a collective risk model with dependence involving the family of multivariate mixed Erlang distributions. Other models based on mixtures involving bivariate and multivariate copulas in a more general setting are then presented. These different structures allow to link the number of claims to each claim amount, and to quantify the aggregate claim loss. Then, we use Archimedean and hierarchical Archimedean copulas in collective risk models, to model the dependence between the claim number random variable and the claim amount random variables involved in the random sum. Such dependence structures allow us to derive a computational methodology for the assessment of the aggregate claim amount. While being very flexible, this methodology is easy to implement, and can easily fit more complicated hierarchical structures.

Survival data or more general time-to-event data occur in many areas, including medicine, biology, engineering, economics, and demography, but previously standard methods have requested that all time variables are univariate and independent. This book extends the field by allowing for multivariate times. As the field is rather new, the concepts and the possible types of data are described in detail. Four different approaches to the analysis of such data are presented from an applied point of view.

Multivariate Survival Analysis and Competing Risks introduces univariate survival analysis and extends it to the multivariate case. It covers competing risks and counting processes and provides many real-world examples, exercises, and R code. The text discusses survival data, survival distributions, frailty models, parametric methods, multivariate data and distributions, copulas, continuous failure, parametric likelihood inference, and non- and semi-parametric methods. There are many books covering survival analysis, but very few that cover the multivariate case in any depth. Written for a graduate-level audience in statistics/biostatistics, this book includes practical exercises and R code for the examples. The author is renowned for his clear writing style, and this book continues that trend. It is an excellent reference for graduate students and researchers looking for grounding in this burgeoning field of research.