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Book Description

Focusing on what actuaries need in practice, this introductory account provides readers with essential tools for handling complex problems and explains how simulation models can be created, used and re-used (with modifications) in related situations. The book begins by outlining the basic tools of modelling and simulation, including a discussion of the Monte Carlo method and its use. Part II deals with general insurance and Part III with life insurance and financial risk. Algorithms that can be implemented on any programming platform are spread throughout and a program library written in R is included. Numerous figures and experiments with R-code illustrate the text. The author's non-technical approach is ideal for graduate students, the only prerequisites being introductory courses in calculus and linear algebra, probability and statistics. The book will also be of value to actuaries and other analysts in the industry looking to update their skills.

1. Cover
2. Half Title
3. Series
4. Title
6. Contents
7. Preface
8. 1 Introduction
1. 1.1 A view on the evaluation of risk
2. 1.2 Insurance risk: Basic concepts
3. 1.3 Financial risk: Basic concepts
4. 1.4 Risk over time
5. 1.5 Method: A unified beginning
6. 1.6 How the book is planned
7. 1.7 Bibliographical notes
9. PART I TOOLS FOR RISK ANALYSIS
1. 2 Getting started the Monte Carlo way
1. 2.1 Introduction
2. 2.2 How simulations are used
3. 2.3 How random variables are sampled
4. 2.4 Making the Gaussian work
5. 2.5 Positive random variables
6. 2.6 Mathematical arguments
7. 2.7 Bibliographical notes
8. 2.8 Exercises
2. 3 Evaluating risk: A primer
1. 3.1 Introduction
2. 3.2 General insurance: Opening look
3. 3.3 How Monte Carlo is put to work
4. 3.4 Life insurance: A different story
5. 3.5 Financial risk: Derivatives as safety
6. 3.6 Risk over long terms
7. 3.7 Mathematical arguments
8. 3.8 Bibliographical notes
9. 3.9 Exercises
3. 4 Monte Carlo II: Improving technique
1. 4.1 Introduction
2. 4.2 Table look-up methods
3. 4.3 Correlated sampling
4. 4.4 Importance sampling and rare events
5. 4.5 Control variables
6. 4.6 Random numbers: Pseudo- and quasi-
7. 4.7 Mathematical arguments
8. 4.8 Bibliographical notes
9. 4.9 Exercises
4. 5 Modelling I: Linear dependence
1. 5.1 Introduction
2. 5.2 Descriptions of first and second order
3. 5.3 Financial portfolios and Markowitz theory
4. 5.4 Dependent Gaussian models once more
5. 5.5 The random walk
6. 5.6 Introducing stationary models
7. 5.7 Changing the time scale
8. 5.8 Mathematical arguments
9. 5.9 Bibliographical notes
10. 5.10 Exercises
5. 6 Modelling II: Conditional and non-linear
1. 6.1 Introduction
2. 6.2 Conditional modelling
3. 6.3 Uncertainty on different levels
4. 6.4 The role of the conditional mean
5. 6.5 Stochastic dependence: General
6. 6.6 Markov chains and life insurance
7. 6.7 Introducing copulas
8. 6.8 Mathematical arguments
9. 6.9 Bibliographical notes
10. 6.10 Exercises
6. 7 Historical estimation and error
1. 7.1 Introduction
2. 7.2 Error of different origin
3. 7.3 How parameters are estimated
4. 7.4 Evaluating error I
5. 7.5 Evaluating error II: Nested schemes
6. 7.6 The Bayesian approach
7. 7.7 Mathematical arguments
8. 7.8 Bibliographical notes
9. 7.9 Exercises
10. PART II GENERAL INSURANCE
1. 8 Modelling claim frequency
1. 8.1 Introduction
2. 8.2 The world of Poisson
3. 8.3 Random intensities
4. 8.4 Intensities with explanatory variables
5. 8.5 Modelling delay
6. 8.6 Mathematical arguments
7. 8.7 Bibliographical notes
8. 8.8 Exercises
2. 9 Modelling claim size
1. 9.1 Introduction
2. 9.2 Parametric and non-parametric modelling
3. 9.3 The log-normal and Gamma families
4. 9.4 The Pareto families
5. 9.5 Extreme value methods
6. 9.6 Searching for the model
7. 9.7 Mathematical arguments
8. 9.8 Bibliographical notes
9. 9.9 Exercises
3. 10 Solvency and pricing
1. 10.1 Introduction
2. 10.2 Portfolio liabilities by simple approximation
3. 10.3 Portfolio liabilities by simulation
4. 10.4 Differentiated pricing through regression
5. 10.5 Differentiated pricing through credibility
6. 10.6 Reinsurance
7. 10.7 Mathematical arguments
8. 10.8 Bibliographical notes
9. 10.9 Exercises
4. 11 Liabilities over long terms
1. 11.1 Introduction
2. 11.2 Simple situations
3. 11.3 Time variation through regression
4. 11.4 Claims as a stochastic process
5. 11.5 Building simulation models
6. 11.6 Cash flow or book value?
7. 11.7 Mathematical arguments
8. 11.8 Bibliographical notes
9. 11.9 Exercises
11. PART III LIFE INSURANCE AND FINANCIAL RISK
1. 12 Life and state-dependent insurance
1. 12.1 Introduction
2. 12.2 The anatomy of state-dependent insurance
3. 12.3 Survival modelling
4. 12.4 Single-life arrangements
5. 12.5 Multi-state insurance I: Modelling
6. 12.6 Multi-state insurance II: Premia and liabilities
7. 12.7 Mathematical arguments
8. 12.8 Bibliographical notes
9. 12.9 Exercises
2. 13 Stochastic asset models
1. 13.1 Introduction
2. 13.2 Volatility modelling I
3. 13.3 Volatility modelling II: The GARCH type
4. 13.4 Linear dynamic modelling
5. 13.5 The Wilkie model I: Twentieth-century financial risk
6. 13.6 The Wilkie model II: Implementation issues
7. 13.7 Mathematical arguments
8. 13.8 Bibliographical notes
9. 13.9 Exercises
3. 14 Financial derivatives
1. 14.1 Introduction
2. 14.2 Arbitrage and risk neutrality
3. 14.3 Equity options I
4. 14.4 Equity options II: Hedging and valuation
5. 14.5 Interest-rate derivatives
6. 14.6 Mathematical summing up
7. 14.7 Bibliographical notes
8. 14.8 Exercises
4. 15 Integrating risk of different origin
1. 15.1 Introduction
2. 15.2 Life-table risk
3. 15.3 Risk due to discounting and inflation
4. 15.4 Simulating assets protected by derivatives
5. 15.5 Simulating asset portfolios
6. 15.6 Assets and liabilities
7. 15.7 Mathematical arguments
8. 15.8 Bibliographical notes
9. 15.9 Exercises
5. Appendix A Random variables: Principal tools
1. A.1 Introduction
2. A.2 Single random variables
3. A.3 Several random variables jointly
4. A.4 Laws of large numbers
6. Appendix B Linear algebra and stochastic vectors
1. B.1 Introduction
2. B.2 Operations on matrices and vectors
3. B.3 The Gaussian model: Simple theory
7. Appendix C Numerical algorithms: A third tool
1. C.1 Introduction
2. C.2 Cholesky computing
3. C.3 Interpolation, integration, differentiation
4. C.4 Bracketing and bisection: Easy and safe
5. C.5 Optimization: Advanced and useful
6. C.6 Bibliographical notes
12. References
13. Index