Loss Models: From Data to Decisions

TLDR: In this paper, the authors present an inventory of continuous and discrete time-ruiner models for complete and modified data sets, as well as a comprehensive inventory of discrete and continuous distributions for complete data sets.

Abstract: Preface. Acknowledgments. PART I: INTRODUCTION. 1. Modeling. PART II: ACTUARIAL MODELS. 2. Random Variables. 3. Basic Distributional Quantities. 4. Classifying and Creating Distributions. 5. Frequency and Severity with Coverage Modifications. 6. Aggregate Loss Models. 7. Discrete Time Ruin Models. 8. Continuous Time Ruin Models. PART III: CONSTRUCTION OF EMPIRICAL MODELS. 9. Review of Mathematical Statistics. 10. Estimation for Complete Data. 11. Estimation for Modified Data. PART IV: PARAMETRIC STATISTICAL METHODS. 12. Parameter Estimation. 13. Model Selection. 14. Five Examples. PART V: ADJUSTED ESTIMATES AND SIMULATION. 15. Interpolation and Smoothing. 16. Credibility. 17. Simulation. Appendix A: An Inventory of Continuous Distributions. Appendix B: An Inventory of Discrete Distributions. Appendix C: Frequency and Severity Relationships. Appendix D: The Recursive Formula. Appendix E: Discretization of the Serverity Distribution. Appendix F: Numerical Optimization and Solution of Systems. References. Index.