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

Daniela Anna Selch, Matthias Scherer (Autoren)

eBook Download: PDF

2018 | 1st ed. 2018
XII, 158 Seiten
Springer International Publishing (Verlag)
978-3-319-92868-5 (ISBN)

Infos

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.

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. 

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 31.8.2018
• Reihe/Serie: Springer Actuarial
• Reihe/Serie: Springer Actuarial
• Zusatzinfo: XII, 158 p. 29 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management
• Schlagworte: dynamic modelling approach • modelling dependence in claim count data • modelling multiple lines of business in a holistic perspective • modelling multivariate claim count data • multivariate Cox process • multivariate Lévy subordinator • over-dispersion in claim count data • Quantitative Finance • reinsurance contracts pricing • simultaneous jump arrivals
• ISBN-10: 3-319-92868-6 / 3319928686
• ISBN-13: 978-3-319-92868-5 / 9783319928685