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Financial and Actuarial Statistics

An Introduction, Second Edition

By Dale S. Borowiak, Arnold F. Shapiro

Chapman and Hall/CRC – 2013 – 392 pages

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    978-1-42-008580-8
    November 12th 2013

Description

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.

Contents

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.

Author Bio

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.

Name: Financial and Actuarial Statistics: An Introduction, Second Edition (Hardback)Chapman and Hall/CRC 
Description: By Dale S. Borowiak, Arnold F. Shapiro. 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...
Categories: Financial Mathematics, Statistics, Finance