R Programming for Actuarial Science

About the Companion Website xxi

Introduction 1

1 R : What You Need to Know to Get Started 9

2 Functions in R 33

3 Financial Mathematics (1): Interest Rates and Valuing Cashflows 45

4 Financial Mathematics (2): Miscellaneous Examples 63

5 Fundamental Statistics: A Selection of Key Topics -- Dr A Kume 87

6 Multivariate Distributions, and Sums of Random Variables 139

7 Benefits of Diversification 147

8 Modern Portfolio Theory 155

9 Duration -- A Measure of Interest Rate Sensitivity 171

10 Asset-Liability Matching: An Introduction 177

11 Hedging: Protecting Against a Fall in Equity Markets 187

12 Immunisation -- Redington and Beyond 195

13 Copulas 211

14 Copulas -- A Modelling Exercise 237

15 Bond Portfolio Valuation: A Simple Credit Risk Model 247

16 The Markov 2-State Mortality Model 259

17 Approaches to Fitting Mortality Models: The Markov 2-state Model and an Introduction to Splines 273

18 Assessing the Suitability of Mortality Models: Statistical Tests 295

19 The Lee-Carter Model 311

20 The Kaplan-Meier Estimator 329

21 Cox Proportionate Hazards Regression Model 339

22 Markov Multiple State Models: Applications to Life Contingencies 351

23 Contingencies I 383

24 Contingencies II 403

25 Actuarial Risk Theory -- An Introduction: Collective and Individual Risk Models 447

26 Collective Risk Models: Exercise 473

27 Generalised Linear Models: Poisson Regression 481

28 Extreme Value Theory 501

29 Introduction to Machine Learning: k-Nearest Neighbours (kNN) 513

30 Time Series Modelling in R -- Dr A Kume 523

31 Volatility Models -- GARCH 551

32 Modelling Future Stock Prices Using Geometric Brownian Motion: An Introduction 571

33 Financial Options: Pricing, Characteristics, and Strategies 585

Index 605