A Multivariate Claim Count Model for Applications in Insurance (eBook)

Daniela Selch currently works as a quantitative analyst for the Equities – Structured Products and Strategies team of Barclays Quantitative Analytics in London. Previously, she was a research assistant at the Chair of Mathematical Finance at the Technical University of Munich, where she earned her PhD for the results summarized in this book. Her PhD thesis was awarded the SCOR-price for actuarial sciences and she presented at several scientific conferences, including the ICBI Global Derivatives Trading & Risk Management 2016, Budapest as invited speaker.Matthias Scherer is Professor for Financial Mathematics at the Technical University of Munich, member of the board of the German Society for Insurance and Financial Mathematics (DGVFM), and associate editor of the journals Dependence Modelling and RISIKO MANAGER. He has (co-)authored scientific papers in the areas finance and actuarial science, multivariate statistics, probability theory, and quantitative risk management. 

Preface 7
Acknowledgements 8
Contents 9
1 Motivation and Model 11
1.1 Model Setup: Notation and Assumptions 12
1.2 Arrival Times and Simulation 16
1.3 Literature Review 19
2 Properties of the Model 23
2.1 Process Distribution 23
2.2 Lévy and Compound Poisson Characterization 53
2.3 Large Portfolio Approximation 76
3 Estimation of the Parameters 83
3.1 Estimation Procedures 83
3.1.1 Discrete Monitoring 85
3.1.2 Continuous Monitoring 88
3.2 Simulation Study 92
3.2.1 Setting: Inverse Gaussian Subordinator (No Drift) 95
3.2.2 Setting: Inverse Gaussian Subordinator with Drift 98
3.2.3 Summary 103
3.3 Real-World Data Example 106
4 Applications and Extensions 121
4.1 Premium Calculation and Dependence Ordering 121
4.1.1 Compound Model and Direct Insurer 123
4.1.2 Stop-Loss Order and Reinsurer 128
4.2 Model Extensions 140
4.2.1 Compound Model 140
4.2.2 Deterministic Time-Change 142
4.2.3 Multivariate Subordination 143
5 Appendix: Technical Background 147
5.1 The Poisson Process and its Generalizations 147
5.2 Lévy Subordinators 154
References 161
Index 166