University of Lausanne, Lausanne, Switzerland University Salzburg, Salzburg, Austria

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1 EAA Series Editors-in-chief Hansjoerg Albrecher Ulrich Orbanz Editors Michael Koller Ermanno Pitacco Christian Hipp Antoon Pelsser Alexander J. McNeil University of Lausanne, Lausanne, Switzerland University Salzburg, Salzburg, Austria ETH Zurich, Zurich, Switzerland Università di Trieste, Trieste, Italy Universität Karlsruhe, Karlsruhe, Germany Maastricht University, Maastricht, The Netherlands Heriot-Watt University, Edinburgh, UK EAA series is successor of the EAA Lecture Notes and supported by the European Actuarial Academy (EAA GmbH), founded on the 29 August, 2005 in Cologne (Germany) by the Actuarial Associations of Austria, Germany, the Netherlands and Switzerland. EAA offers actuarial education including examination, permanent education for certified actuaries and consulting on actuarial education. actuarial-academy.com For further titles published in this series, please go to

2 Marcus Kriele Jochen Wolf Value-Oriented Risk Management of Insurance Companies

3 Marcus Kriele Hoboken, NJ, USA Jochen Wolf Fachbereich Mathematik und Technik Hochschule Koblenz Remagen, Germany Translation from the German language edition: Wertorientiertes Risikomanagement von Versicherungsunternehmen by Marcus Kriele and Jochen Wolf Copyright Springer Verlag Berlin Heidelberg 2012 ALL RIGHTS RESERVED Additional material to this book can be downloaded from ISSN ISSN (electronic) EAA Series ISBN ISBN (ebook) DOI / Springer London Heidelberg New York Dordrecht Library of Congress Control Number: Mathematics Subject Classification: 91B30, 91B70 Springer-Verlag London 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (

4 Preface to the English Edition The English edition differs from the German original in that we have changed parts of the presentation in order to better address international readers. We have corrected any errors we are aware of. Some sections have been somewhat expanded, most notably the section on the Swiss Solvency Test (SST). The SST is a working example of a modern, economic capital based implementation for regulatory capital requirements. This book contains example scripts using the statistical language R. These files can be downloaded from using the ISBN of this book. We would like to thank Springer-Verlag for suggesting an English version of our book and for having the German text translated. We would also like thank our translator, Patrick Ion, who not only translated the whole text but who, on many occasions, also explained to us subtleties of the English language. Hoboken, NJ, USA Remagen, Germany September 2013 Marcus Kriele Jochen Wolf v

5 Preface Value- and risk-oriented management is a holistic method of managing businesses. This method comprises components that belonged classically to internal control or the actuarial department, so that we need an approach that crosses the boundaries of subjects. As a result of the emphasis on the measurement of risks we find a new dynamically developing area of problems for actuaries. In this book we try to provide the required basic knowledge for this from an actuarial perspective. Our language is thus that of mathematicians. To communicate within an insurance company, between technical and non-technical departments, the concepts introduced must naturally be translated into ordinary language. It is part of an actuary s job to ensure that in this translation the essence of the assertions remains without making unreasonable mathematical demands upon the reader. As each measurement has associated with it measurement errors, as well as modeling errors, it was of special importance to us in showing the limitations of the methods we present. The book before you was developed as a text for the Value-oriented Risk Management [German: Wertorientiertes Risikomanagement ] module of the actuarial course of the German Actuarial Society [German: Deutsche Aktuarvereinigung e.v. 1 (DAV)] and covers its complete syllabus. However, this book does not depend on other modules and can be read independently of the actuarial course. Furthermore, we have covered a number of additional topics that we consider important, which go beyond the bounds of a DAV-module. Chapter 7 on value-oriented business management includes exercises that are intended to encourage the reader to particularly intensive work on this area. For most of the exercises there is more than one solution. The book includes examples of code written in the scripting environment R 2 used for programming in statistics. R is Open Source Software licensed under a GNU R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, vii

6 viii Preface license 3 and is available for download free from the website for the common operating systems Linux, OS X, and Windows. Along with the base package we use the copula library 4 which can also be obtained from the same website under a similar license. The code given here is intended for purely educational purposes. The authors explicitly reject any responsibility for its correctness or its usefulness for business management. We wrote and revised this book together. However, for each section one of the authors does feel a special responsibility. Marcus Kriele: 2, 3, 4.1, 4.3, 4.4.3, 4.5, 4.6, 5, 6, 7 Jochen Wolf: 1, 4.2, 4.4, 4.5.3, 8 In writing this book we have made extensive use of Open Source Software, in particular of the typesetting program LATEX, 5 of the text preparation program LYX 6 based on LATEX, of the LATEX graphics package TikZ, 7 of the editor Emacs 8 /Aquamacs 9 and also of R. We are especially grateful to the developers who have made available to the community such mature tools. We would like to heartily thank Guido Bader for his many remarks and suggestions for improvements. Special thanks go to Damir Filipović. This book is based on notes that we wrote together. Section is an extension of an original version written by him, and Section 5.3 is adopted unchanged from him. Furthermore, we were able to improve our text greatly as a result of his comments and much discussion with him. The ideas put forward here do not necessarily reflect the opinions of our employers, present or previous. In particular, readers interested in German or Swiss insurance supervision should take into account the official views and regulations of the BaFin or FINMA on their websites and in their publications. New York, USA Remagen, Germany October 2011 Marcus Kriele Jochen Wolf 3 The R Core Team is of the opinion that this license allows the use of R and R-packages for commercial purposes (including consulting). 4 J. Yan and I. Kojadinovic, Modeling multivariate distributions with continuous margins using the copula R-package. Statistical Software 34(9), 1 20 (2010). 5 F. Mittelbach, M. Goossens, J. Braams, D. Carlisle, and C. Rowley, The LATEX Companion. Addison-Wesley Series on Tools and Techniques for Computer Typesetting. Addison-Wesley Professional, Boston (2004). 6 The LyX Team, LyX 2.0.x The document processor. (2011). 7 T. Tantau, The TikZ and PGF packages. Universität zu Lübeck, Institut für Theoretische Informatik (2010). 8 Gnu Emacs Developers, Emacs 23.x (2009). 9 Aquamacs Developers, Aquamacs 2.x (2010).

7 Contents 1 The Process of Risk Management Risks and Opportunities CompilationandIdentificationofRisks EvaluatingRisks Response to Risk AvoidingRisks Reduction of Risks TransferofRisks MonitoringRisk The Role of the Appointed Actuary in the Risk Management Process References Risk Measures TheNotionofaRiskMeasure ExamplesofRiskMeasures MeasuresBasedonMoments ValueatRisk Tail Value at Risk and Expected Shortfall Spectral Measures Choosing a Good Risk Measure Risk Measures and the Intuition of Risk PracticalConsiderations Dynamic Risk Measures Filtrations General Dynamic Risk Measures Dynamic Risk Measures on Filtered Product Economies A Class of Dynamic Risk Measures on General Filtrations References ix

8 x Contents 3 Dependencies Diversification Copulas Examples Tail Dependence Modeling with Copulas Correlations Functional Dependencies References Risk Capital RiskCapitalandCostofCapital Risk Capital as a Criterion for Comparing Diverse Risks CostofCapital Risk-BearingCapital Types of Risk Capital Economic Risk Capital RatingCapital SolvencyCapital Valuing Insurance Liabilities Concept and Definition Approaches to Valuation of Insurance Liabilities Implementation Concepts Valuing Technical Provisions According to IFRS Approaches to Modeling Risk Capital Factor-Based Models Analytic Models Scenario-Based Models and Stress Tests Monte Carlo Models The Problem of Modeling Reinsurance Feedback of Investment Risk on Capital Risk Capital Models in Practice TheSwissSolvencyTest(SST) The Standard Model in Solvency II References Allocation of Capital Introduction Examples Proportional Capital Allocation MarginalPrinciples Game-Theoretic Capital Allocation Principles Kalkbrener s Axioms Capital Allocation for Groups References

9 Contents xi 6 Performance Measurement Performance Measurement Based on Balance Sheets ProfitMeasurement Absolute Performance Measures Relative Performance Measures ANumericalExample BasicsofCompanyValuation Various Perspectives for Company Valuation DeterministicValuation CostofCapitalBasedValuation MarketConsistentValuation Key Performance Indicators and Constraints Differing Requirements in Life Insurance and Non-life Insurance 268 References Value-Oriented Company Management The Concept of Value-Oriented Company Management The Strategic Component The Measurement Component The Organizational Component The Process Component Objective Setting and Supervision: Balanced Scorecard AnExampleCompany Definition of Business Areas Subject to Risk Oriented Management Mitigation of Risks for which Economic Capital is Only PartlySuitable The Economic Capital Model of XYZ Inc Criticism of the Capital Model for XYZ Inc Indicators The Organizational Components for Value-Oriented Management at XYZ Inc The Process Components of Value-Oriented Management atxyzinc References Solvency and Regulatory Questions Law Regulating Control and Transparency in Business (KonTraG) GoalsofKonTraG Regulations Implementation Solvency The Task of Solvency Supervision Definitions SolvencyI

10 xii Contents SolvencyII References Appendix A The Capital Asset Pricing Model (CAPM) Appendix B R-Code for the SST Calculation Using the delta-gamma-model Appendix C R-Script for the Scenario-Based Solvency II SCR Computation Appendix D R-Script for the Solvency II SCR Computation forxyzincinexample D.1 Input Definition D.2 ComputingtheSCR D.3 OutputfromtheComputation Appendix E R-Script of the Simplified Economic Capital Model E.1 Input Definition E.2 Computation of the Economic Capital E.3 OutputfromtheComputation Index