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Reinsurance

Book Description

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.

Table of Contents

  1. Cover
  2. Title Page
  3. Preface
  4. 1 Introduction
    1. 1.1 What is Reinsurance?
    2. 1.2 Why Reinsurance?
    3. 1.3 Reinsurance Data
    4. 1.4 Notes and Bibliography
  5. 2 Reinsurance Forms and their Properties
    1. 2.1 Quota‐share Reinsurance
    2. 2.2 Surplus Reinsurance
    3. 2.3 Excess‐of‐loss Reinsurance
    4. 2.4 Stop‐loss Reinsurance
    5. 2.5 Large Claim Reinsurance
    6. 2.6 Combinations of Reinsurance Forms and Global Protections
    7. 2.7 Facultative Contracts
    8. 2.8 Notes and Bibliography
  6. 3 Models for Claim Sizes
    1. 3.1 Tails of Distributions
    2. 3.2 Large Claims
    3. 3.3 Common Claim Size Distributions
    4. 3.4 Mean Excess Analysis
    5. 3.5 Full Models: Splicing
    6. 3.6 Multivariate Modelling of Large Claims
  7. 4 Statistics for Claim Sizes
    1. 4.1 Heavy or Light Tails: QQ‐ and Derivative Plots
    2. 4.2 Large Claims Modelling through Extreme Value Analysis
    3. 4.3 Global Fits: Splicing, Upper‐truncation and Interval Censoring
    4. 4.4 Incorporating Covariate Information
    5. 4.5 Multivariate Analysis of Claim Distributions
    6. 4.6 Estimation of Other Tail Characteristics
    7. 4.7 Further Case Studies
    8. 4.8 Notes and Bibliography
  8. 5 Models for Claim Counts
    1. 5.1 General Treatment
    2. 5.2 The Poisson Process and its Extensions
    3. 5.3 Other Claim Number Processes
    4. 5.4 Discrete Claim Counts
    5. 5.5 Statistics of Claim Counts
    6. 5.6 Claim Numbers under Reinsurance
    7. 5.7 Notes and Bibliography
  9. 6 Total Claim Amount
    1. 6.1 General Formulas for Aggregating Independent Risks
    2. 6.2 Classical Approximations for the Total Claim Size
    3. 6.3 Panjer Recursion
    4. 6.4 Fast Fourier Transform
    5. 6.5 Total Claim Amount under Reinsurance
    6. 6.6 Numerical Illustrations
    7. 6.7 Aggregation for Dependent Risks
    8. 6.8 Notes and Bibliography
  10. 7 Reinsurance Pricing
    1. 7.1 Classical Principles of Premium Calculation
    2. 7.2 Solvency Considerations
    3. 7.3 Pricing Proportional Reinsurance
    4. 7.4 Pricing Non‐proportional Reinsurance
    5. 7.5 The Aggregate Risk Margin
    6. 7.6 Leading and Following Reinsurers
    7. 7.7 Notes and Bibliography
  11. 8 Choice of Reinsurance
    1. 8.1 Decision Criteria
    2. 8.2 Classical Optimality Results
    3. 8.3 Solvency Constraints and Cost of Capital
    4. 8.4 Minimizing Other Risk Measures
    5. 8.5 Combining Reinsurance Treaties
    6. 8.6 Reinsurance Chains
    7. 8.7 Dynamic Reinsurance
    8. 8.8 Beyond Piecewise Linear Contracts
    9. 8.9 Notes and Bibliography
  12. 9 Simulation
    1. 9.1 The Monte Carlo Method
    2. 9.2 Variance Reduction Techniques
    3. 9.3 Quasi‐Monte Carlo Techniques
    4. 9.4 Notes and Bibliography
  13. 10 Further Topics
    1. 10.1 More on Large Claim Reinsurance
    2. 10.2 Alternative Risk Transfer
    3. 10.3 Reinsurance and Finance
    4. 10.4 Catastrophic Risk
  14. References
  15. Index
  16. End User License Agreement