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