Borowiak / Shapiro Financial and Actuarial Statistics

An Introduction, Second Edition
2. Auflage 2013
ISBN: 978-1-135-54104-0
Verlag: Taylor & Francis
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 392 Seiten

Understand Up-to-Date Statistical Techniques for Financial and Actuarial Applications

Since the first edition was published, statistical techniques, such as reliability measurement, simulation, regression, and Markov chain modeling, have become more prominent in the financial and actuarial industries. Consequently, practitioners and students must acquire strong mathematical and statistical backgrounds in order to have successful careers.

Financial and Actuarial Statistics: An Introduction, Second Edition enables readers to obtain the necessary mathematical and statistical background. It also advances the application and theory of statistics in modern financial and actuarial modeling. Like its predecessor, this second edition considers financial and actuarial modeling from a statistical point of view while adding a substantial amount of new material.

New to the Second Edition

- Nomenclature and notations standard to the actuarial field

- Excel exercises with solutions, which demonstrate how to use Excel functions for statistical and actuarial computations

- Problems dealing with standard probability and statistics theory, along with detailed equation links

- A chapter on Markov chains and actuarial applications

- Expanded discussions of simulation techniques and applications, such as investment pricing

- Sections on the maximum likelihood approach to parameter estimation as well as asymptotic applications

- Discussions of diagnostic procedures for nonnegative random variables and Pareto, lognormal, Weibull, and left truncated distributions

- Expanded material on surplus models and ruin computations

- Discussions of nonparametric prediction intervals, option pricing diagnostics, variance of the loss function associated with standard actuarial models, and Gompertz and Makeham distributions

- Sections on the concept of actuarial statistics for a collection of stochastic status models

The book presents a unified approach to both financial and actuarial modeling through the use of general status structures. The authors define future time-dependent financial actions in terms of a status structure that may be either deterministic or stochastic. They show how deterministic status structures lead to classical interest and annuity models, investment pricing models, and aggregate claim models. They also employ stochastic status structures to develop financial and actuarial models, such as surplus models, life insurance, and life annuity models.

Autoren/Hrsg.

Borowiak, Dale S.

Shapiro, Arnold F.

Fachgebiete

• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Versicherungswirtschaft
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Finanz- und Versicherungsmathematik
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

Statistical Concepts
Probability
Random Variables
Expectations
Moment Generating Function
Survival Functions
Nonnegative Random Variables
Conditional Distributions
Joint Distributions

Statistical Techniques
Sampling Distributions and Estimation
Sums of Independent Variables
Order Statistics and Empirical Prediction Intervals
Approximating Aggregate Distributions
Compound Aggregate Variables
Regression Modeling
Autoregressive Systems
Model Diagnostics

Financial Computational Models
Fixed Financial Rate Models
Fixed-Rate Annuities
Stochastic Rate Models

Deterministic Status Models
Basic Loss Model
Stochastic Loss Criterion
Single-Risk Models
Collective Aggregate Models
Stochastic Surplus Model

Future Lifetime Random Variables and Life Tables
Continuous Future Lifetime
Discrete Future Lifetime
Force of Mortality
Fractional Ages
Select Future Lifetimes
Survivorship Groups
Life Models and Life Tables
Life Table Confidence Sets and Prediction Intervals
Life Models and Life Table Parameters
Select and Ultimate Life Tables

Stochastic Status Models
Stochastic Present Value Functions
Risk Evaluations
Percentile Evaluations
Life Insurance
Life Annuities
Relating Risk Calculations
Actuarial Life Tables
Loss Models and Insurance Premiums
Reserves
General Time Period Models
Expense Models and Computations

Advanced Stochastic Status Models
Multiple Future Lifetimes
Multiple-Decrement Models
Pension Plans

Markov Chain Methods
Introduction to Markov Chains
Nonhomogeneous Stochastic Status Chains
Homogeneous Stochastic Status Chains
Survivorship Chains

Scenario and Simulation Testing
Scenario Testing
Simulation Techniques
Investment Pricing Applications
Stochastic Surplus Application
Future Directions in Simulation Analysis

Further Statistical Considerations
Mortality Adjustment Models
Mortality Trend Modeling
Actuarial Statistics
Data Set Simplifications

Appendix A: Excel Statistical Functions, Basic Mathematical Functions, and Add-Ins
Appendix B: Acronyms and Principal Sections

References

Subject Index

Index

Problems, Excel Problems, and Solutions appear at the end of each chapter.

Über Autor(innen)

Dale S. Borowiak is a Professor Emeritus at the University of Akron, where he served for 35 years teaching statistics and initiating the actuarial science program. He received a Ph.D. from Bowling Green State University. His research has been published in professional journals in the fields of statistics, actuarial science, and engineering. He also published Model Discrimination for Nonlinear Regression Models, along with the first edition of the current text.

Arnold F. Shapiro is a Professor Emeritus at the Pennsylvania State University, where he was director of the actuarial program. He received a Ph. D. from the University of Pennsylvania (Wharton). He has published more than 100 articles in professional journals and two books. A Fellow of the Society of Actuaries and an Enrolled Actuary, he been a recipient of the Innovation in Teaching Award from the American Risk and Insurance Association and the Best Research Paper Award from the Health Section of the Society of Actuaries.