This monograph presents a time-dynamic model for multivariate claim counts in actuarial applications. Inspired by real-world claim arrivals, the model balances interesting stylized facts (such as dependence across the components, over-dispersion and the clustering of claims) with a high level of mathematical tractability (including estimation, sampling and convergence results for large portfolios) and can thus be applied in various contexts (such as risk management and pricing of (re-)insurance contracts). The authors provide a detailed analysis of the proposed probabilistic model, discussing its relation to the existing literature, its statistical properties, different estimation strategies as well as possible applications and extensions. Actuaries and researchers working in risk management and premium pricing will find this book particularly interesting. Graduate-level probability theory, stochastic analysis and statistics are required.

Reinsurance: Actuarial and Statistical Aspects provides a survey of both the academic literature in the field as well as challenges appearing in reinsurance practice and puts the two in perspective. The book is written for researchers with an interest in reinsurance problems, for graduate students with a basic knowledge of probability and statistics as well as for reinsurance practitioners. The focus of the book is on modelling together with the statistical challenges that go along with it. The discussed statistical approaches are illustrated alongside six case studies of insurance loss data sets, ranging from MTPL over fire to storm and flood loss data. Some of the presented material also contains new results that have not yet been published in the research literature. An extensive bibliography provides readers with links for further study.

"Offers a mathematical introduction to non-life insurance and, at the same time, to a multitude of applied stochastic processes. It gives detailed discussions of the fundamental models for claim sizes, claim arrivals, the total claim amount, and their probabilistic properties....The reader gets to know how the underlying probabilistic structures allow one to determine premiums in a portfolio or in an individual policy." --Zentralblatt für Didaktik der Mathematik

An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents recent methods and algorithms, including the multilevel Monte Carlo method, the statistical Rom

The recent global financial crisis has forced a re-examination of risk transmission in the financial sector and how it affects financial stability. Current macroprudential policy and surveillance (MPS) efforts are aimed establishing a regulatory framework that helps mitigate the risk from systemic linkages with a view towards enhancing the resilience of the financial sector. This paper presents a forward-looking framework ("Systemic CCA") to measure systemic solvency risk based on market-implied expected losses of financial institutions with practical applications for the financial sector risk management and the system-wide capital assessment in top-down stress testing. The suggested approach uses advanced contingent claims analysis (CCA) to generate aggregate estimates of the joint default risk of multiple institutions as a conditional tail expectation using multivariate extreme value theory (EVT). In addition, the framework also helps quantify the individual contributions to systemic risk and contingent liabilities of the financial sector during times of stress.

Applied Predictive Modeling covers the overall predictive modeling process, beginning with the crucial steps of data preprocessing, data splitting and foundations of model tuning. The text then provides intuitive explanations of numerous common and modern regression and classification techniques, always with an emphasis on illustrating and solving real data problems. The text illustrates all parts of the modeling process through many hands-on, real-life examples, and every chapter contains extensive R code for each step of the process. This multi-purpose text can be used as an introduction to predictive models and the overall modeling process, a practitioner’s reference handbook, or as a text for advanced undergraduate or graduate level predictive modeling courses. To that end, each chapter contains problem sets to help solidify the covered concepts and uses data available in the book’s R package. This text is intended for a broad audience as both an introduction to predictive models as well as a guide to applying them. Non-mathematical readers will appreciate the intuitive explanations of the techniques while an emphasis on problem-solving with real data across a wide variety of applications will aid practitioners who wish to extend their expertise. Readers should have knowledge of basic statistical ideas, such as correlation and linear regression analysis. While the text is biased against complex equations, a mathematical background is needed for advanced topics.