R programming for actuarial science / Peter McQuire, Alfred Kume.

Format:

Book

Author/Creator:

McQuire, Peter, author.

Contributor:

Kume, Alfred.

Language:

English

Subjects (All):

R (Computer program language).

Actuarial science.

Physical Description:

1 online resource illustrations.

Edition:

1st edition

Place of Publication:

Newark : John Wiley & Sons, Incorporated, 2023.

Summary:

"The purpose of this chapter is to introduce the fundamentals of the R programming language, and the basic tools you will need to use this book; it is therefore an important chapter for readers new to R. The reader is advised, following reading this chapter, to proceed to Chapter 2 which, together with this chapter, forms our introduction to programming in R. R is an exceptional statistical computing tool which is increasingly used by researchers and students in many disciplines. R is an open-source language which one can use without purchasing a licence, and contribute to solving problems within the vast R community."-- Provided by publisher.

Contents:

Intro

R Programming for Actuarial Science

Contents

About the Companion Website

Introduction

1 Main Objectives of This Book

2 Who Is This Book For?

3 How to Use This Book

4 Book Structure

5 Chapter Style

6 Examples and Exercises

7 Verification of Code and Calculations - Best Practice

8 Website: www.wiley.com/go/rprogramming.com

9 R or Microsoft Excel?

10 Caveats

11 Acknowledgements

1 R : What You Need to Know to Get Started

1.1 Introduction

1.2 Getting Started: Installation of R and RStudio

1.2.1 Installing R

1.2.2 What Is RStudio?

1.2.3 Inputting R Commands

1.3 Assigning Values

1.4 Help in R

1.5 Data Objects in R

1.6 Vectors

1.6.1 Numeric Vectors

1.6.2 Logical Vectors

1.6.3 Character Vectors

1.6.4 Factor Vectors

1.7 Matrices

1.8 Dataframes

1.9 Lists

1.10 Simple Plots and Histograms

1.11 Packages

1.12 Script Files

1.13 Workspace, Saving Objects, and Miscellany

1.14 Setting YourWorking Directory

1.15 Importing and Exporting Data

1.15.1 Importing Data

1.15.2 Exporting Data

1.16 Common Errors Made in Coding

1.17 Next Steps

1.18 Recommended Reading

1.19 Appendix: Coercion

2 Functions in R

2.1 Introduction

2.1.1 Objectives

2.1.2 Core and Package Functions

2.1.3 User-Defined Functions

2.2 An Introduction to Applying Core and Package Functions

2.2.1 Examples of Simple, Common Functions

2.3 User-Defined Functions

2.3.1 What does a "udf" consist of?

2.3.2 Naming Conventions

2.3.3 Examples and Exercises

2.4 Using Loops in R - the "for" Function

2.5 Integral Calculus in R

2.5.1 The "Integrate" Function

2.5.2 Numerical Integration

2.6 Recommended Reading

3 Financial Mathematics (1): Interest Rates and Valuing Cashflows

3.1 Introduction

3.2 The Force of Interest.

3.3 Present Value of Future Cashflows

3.4 Instantaneous Forward Rates and Spot Rates

3.5 Non-Constant Force of Interest

3.5.1 Discrete Cashflows

3.5.2 Cashflows Which Are Continuous

3.6 Effective and Nominal Rates of Interest

3.6.1 Effective Rates of Interest

3.6.2 Why DoWe Use Effective Rates?

3.6.3 Nominal Interest Rates

3.7 Appendix: Force of Interest - An Analogy with Mortality Rates

3.8 Recommended Reading

4 Financial Mathematics (2): Miscellaneous Examples

4.1 Introduction

4.2 Writing Annuity Functions

4.2.1 Writing a function for an annuity certain

4.3 The 'presentValue' Function

4.4 Annuity Function

4.5 Bonds - Pricing and Yield Calculations

4.6 Bond Pricing: Non-Constant Interest Rates

4.7 The Effect of Future Yield Changes on Bond Prices Throughout the Term of the Bond

4.8 Loan Schedules

4.8.1 Introduction

4.8.2 Method 1

4.8.3 Method 2

4.9 Recommended Reading

5 Fundamental Statistics: A Selection of Key Topics

5.1 Introduction

5.2 Basic Distributions in Statistics

5.3 Some Useful Functions for Descriptive Statistics

5.3.1 Introduction

5.3.2 Bivariate or Higher Order Data Structure

5.4 Statistical Tests

5.4.1 Exploring for Normality or Any Other Distribution in the Data

5.4.2 Goodness-of-fit Testing for Fitted Distributions to Data

5.4.2.1 Continuous distributions

5.4.2.2 Discrete distributions

5.4.3 T-tests

5.4.3.1 One sample test for the mean

5.4.3.2 Two sample tests for the mean

5.4.4 F-test for Equal Variances

5.5 Main Principles of Maximum Likelihood Estimation

5.5.1 Introduction

5.5.2 MLE of the Exponential Distribution

5.5.2.1 Obtaining the MLE numerically using R

5.5.2.2 Obtaining the MLE analytically

5.5.3 Large Sample (Asymptotic) Properties of MLE.

5.5.4 Fitting Distributions to Data in R Using MLE

5.5.5 Likelihood Ratio Test, LRT

5.6 Regression: Basic Principles

5.6.1 Simple Linear Regression

5.6.2 Quantifying Uncertainty on

5.6.3 Analysis of Variance in Regression

5.6.3.1 R2 and adjusted R2 Coefficient of Determination

5.6.4 Some Visual Diagnostics for the Proposed Simple Regression Model

5.7 Multiple Regression

5.7.1 Introduction

5.7.2 Regression and MLE

5.7.2.1 Multivariate Regression

5.7.3 Tests

5.7.3.1 Likelihood Ratio Test in Regression

5.7.3.2 Akaike Information Criterion: AIC

5.7.3.3 AIC and Regression model selection

5.7.3.4 Bayesian Information Criterion: BIC

5.7.4 Variable Selection, Finding the Most Appropriate Sub-Model

5.7.5 Backward Elimination

5.7.6 Forward Selection

5.7.7 Using AIC/BIC Criteria

5.7.8 LRT in Model Selection

5.7.9 Automatic Search Using R-squared Criteria

5.7.10 Concluding Remarks on Test Data

5.7.11 Modelling Beyond Linearity

5.8 Dummy/Indicator Variable Regression

5.8.1 Introducing Categorical Variables

5.8.2 Continuous and Indicator Variable Predictors - Including Load in the Model

5.9 Recommended Reading

6 Multivariate Distributions, and Sums of Random Variables

6.1 Multivariate Distributions - Examples in Finance

6.2 Simulating Multivariate Normal Variables

6.3 The Summation of a Number of Random Variables

6.4 Conclusion

6.5 Recommended Reading

7 Benefits of Diversification

7.1 Introduction

7.2 Background

7.3 Key Mathematical Ideas

7.4 Running Simulations

7.5 Recommended Reading

8 Modern Portfolio Theory

8.1 Introduction

8.2 2-Asset Portfolio

8.3 3-Asset Portfolio

8.4 Introduction of a Risk-free Asset to the Portfolio

8.4.1 Adding a Risk-free Asset

8.4.2 Capital Market Line and the Sharpe Ratio.

8.4.3 Borrowing to Obtain Higher Returns

8.5 Appendix: Lagrange Multiplier Method

8.6 Recommended Reading

9 Duration - A Measure of Interest Rate Sensitivity

9.1 Introduction

9.2 Duration - Definitions and Interpretation

9.3 Duration Function in R

9.4 Practical Applications of Duration

9.5 Recommended Reading

10 Asset-Liability Matching: An Introduction

10.1 Introduction

10.2 What Interest Rates Do Institutions Use To Measure Their Liabilities?

10.3 Variance of the Solvency Position

10.4 Characteristics of Various Asset Classes and Liabilities

10.5 Our Scenarios

10.6 Results

10.7 Simulations

10.8 Exercise and Discussion - an Insurer With Predominately Short-Term Liabilities

10.9 Potential Exercise

10.10 Conclusions

10.11 Recommended Reading

11 Hedging: Protecting Against a Fall in Equity Markets

11.1 Introduction

11.2 Our Example

11.2.1 Futures Contracts - A Brief Explanation

11.2.2 Our Task

11.3 Adopting a Better Hedge

11.4 Allowance for Contract and Portfolio Sizes

11.5 Negative Hedge Ratio

11.6 Parameter and Model Risk

11.7 A Final Reminder on Hedging

11.8 Recommended Reading

12 Immunisation - Redington and Beyond

12.1 Introduction

12.2 Outline of Redington Theory and Alternatives

12.3 Redington's Theory of Immunisation

12.4 Changes in the Shape of the Yield Curve

12.5 A More Realistic Example

12.5.1 Determining a Suitable Bond Allocation

12.5.2 Change in Yield Curve Shape

12.5.3 Liquidity Risk

12.6 Conclusion

12.7 Recommended Reading

13 Copulas

13.1 Introduction

13.2 Copula Theory - The Basics

13.3 Commonly Used Copulas

13.3.1 The Independent Copula

13.3.2 The Gaussian Copula

13.3.3 Archimedian Copulas

13.3.4 Clayton Copula

13.3.5 Gumbel Copula

13.4 Copula Density Functions.

13.5 Mapping from Copula Space to Data Space

13.6 Multi-dimensional Data and Copulas

13.7 Further Insight into the Gaussian Copula: A Non-rigorous View

13.8 The Real Power of Copulas

13.9 General Method of Fitting Distributions and Simulations - A Copula Approach

13.9.1 Fitting the Model

13.9.2 Simulating Data Using the mvdc and rMvdc Functions

13.10 How Non-Gaussian Copulas Can Improve Modelling

13.11 Tail Correlations

13.12 Exercise (Challenging)

13.13 Appendix 1 - Copula Properties

13.14 Appendix 2 - Rank Correlation and Kendall's Tau,

13.15 Recommended Reading

14 Copulas - A Modelling Exercise

14.1 Introduction

14.2 Modelling Future Claims

14.2.1 Data

14.2.2 Fitting Appropriate Marginal Distributions

14.2.3 Fitting The Copula

14.2.4 Assessing Risk From the Analysis of Simulated Values

14.2.5 Comparison with the Gaussian Copula Model

14.2.6 Comparison of the Models with the Data

14.3 Another Example: Banking Regulator

14.4 Conclusion

15 Bond Portfolio Valuation: A Simple Credit Risk Model

15.1 Introduction

15.2 Our Example Bond Portfolio

15.2.1 Description

15.2.2 The Transition Matrix

15.2.3 Correlation Matrix

15.2.4 Simulations and Results

15.2.5 Incorporating Interest Rate Risk - A Simple Adjustment

15.2.6 Portfolio Consisting of Highly Correlated Bonds

15.3 Further Development of this Model

15.4 Recommended Reading

16 The Markov 2-State Mortality Model

16.1 Introduction

16.2 Markov 2-State Model

16.3 Simple Applications of the 2-State Model

16.4 Estimating Mortality Rates from Data

16.5 An Example: Calculating Mortality Rates for One Age Band

16.6 Uncertainty in Our Estimates

16.7 Next Steps?

16.8 Appendices

16.8.1 Informal Discussion of

16.8.2 Intuitive meaning of ( )

16.9 Recommended Reading

17 Approaches to Fitting Mortality Models: The Markov 2-state Model and an Introduction to Splines.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: McQuire, Peter R Programming for Actuarial Science

ISBN:

9781119755005

111975500X

9781119754985

1119754984

OCLC:

1406768156