R programming for actuarial science / Peter McQuire, Alfred Kume

R programming for actuarial science / Peter McQuire, Alfred Kume

"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, toget...

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Detalles Bibliográficos
Otros Autores: McQuire, Peter, author (author), Kume, Alfred (-)
Formato: Libro electrónico
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated 2023.
Edición:1st edition
Materias:
R (Computer program language)
Actuarial science.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009811324706719
Tabla de Contenidos:
  • 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.

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