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The overriding objective of this book is to help students of actuarial mathematics and related disciplines such as financial mathematics, develop programming skills which will enhance their understanding of actuarial, financial, and statistical concepts, enabling them to solve real-world problems encountered in these fields. Breaking this down further, the purposes of the book is two-fold:
R
A similar effect is noted in students who opt to take a year out from their studies to work in the financial industry, often applying extensive programming skills to solve real-world problems. Such students invariably notice a similar level of improvement in their understanding of concepts. It is hoped, to some extent, that this learning experience can be mirrored throughout this book.
The authors have significant teaching experience at both undergraduate and postgraduate levels, enhanced with experience in assessment processes for universities and the actuarial profession. This has given insights into the typical issues students experience with actuarial mathematics - problems often arise from a fundamental misunderstanding of introductory material. For example, a final year undergraduate may only fully understand a concept introduced in their first year whilst undertaking programming coursework in their final year on a specific application of the material taught in the first year, experiencing that "Eureka" moment.
The reader should not underestimate the extent to which learning a programming language, such as R, to a level such that most exercises in this book can be completed, will help the reader in the employment market. Having a good working knowledge of R or similar language should improve the career prospects of the graduate.
A further motivating factor for writing this book originates from the decision taken by the Institute and Faculty of Actuaries (IFoA) in 2018 to choose the R programming language as an integral part of its syllabus. Indeed, much of the IFoA's syllabi for subjects CM1, CM2, CS1, and, in particular, CS2 are covered in the book.
This book is aimed at two main groups:
In writing this book, we have attempted to cater for a wide range of experiences and abilities. The overall style of the book aims to ensure that the basics of each topic are covered, with appropriate text, examples, and exercises, whilst including several more advanced tasks. As noted elsewhere, the reader should aim at expanding on the tasks included in this book.
It is assumed that the reader will have a knowledge of statistics and mathematics at a level expected from that of a first year undergraduate in a maths-based university degree.
The book includes the majority of topics covered in a typical undergraduate course in actuarial science. There is also perhaps a greater emphasis placed on a number of actuarial concepts which may not directly be assessed in traditional university courses; indeed, several examples involve addressing practical problems which the student will see in the workplace. For example, we introduce models which may help in improving how correlations are dealt with by insurance companies, and develop an understanding of fundamental risk management techniques such as hedging, asset-liability matching, and diversification. Ultimately, we hope the reader develops a good understanding of the problem-solving approaches used in the workplace.
To get the most from this book it is anticipated that during each study session the user will simultaneously:
It would be expected that the user proceeds to write their own code and duplicate the results. The suggested code for each example/exercise is one of many possible solutions; it may be quite reasonable, depending on the scenario, for your code to be quite different to that set out in this book. It is important that the user practises writing their own, independent code, and does not try to learn, by rote, the code in the book. As noted in Chapter 1, the reader may wish to save a script file in respect of each chapter. Indeed the reader may wish to write functions incorporating and combining several sections of code from the website, improving the efficiency of their code.
We would expect most users to have had some prior exposure to, and knowledge of, the material in a chapter before embarking on it, either following an initial period of independent study, or attendance at related university lectures or tutorials; it is anticipated that readers will have access to alternative study material for each topic.
The website contains the majority of the R code included in the book, together with suggested code relating to the exercises. It is intended that the reader will treat the book and website as companions; it is not expected that most users use the book and website separately (for the most part at least). Note that a small amount of code is not included on the website (the missing code can simply be copied from the book) - this is to encourage more active learning of the material.
The vast majority of students will gain most benefit from frequent practise of writing code; occasional engagement is likely to end in less satisfactory results. It is hoped that the style of the book will lend itself to encouraging a greater level of creativity from the student, developing their own examples and exercises as their skills and knowledge increase.
We start by covering the fundamentals of R in Chapter 1, "R: What you need to know to get started", and Chapter 2, "Functions in R". If you are new to R we recommend that you first read these two chapters, and revisit them when required. Chapter 1 explains the key aspects of R, e.g. writing your first code in R, how objects are used etc. From experience, most students find it beneficial to initially read this chapter relatively quickly, referring back to it frequently. Readers new to R should benefit from spending some time digesting the examples in Chapter 2 to get a feel for writing basic R code and applying existing functions.
The typical actuarial and financial mathematics student is then likely to cover Chapters 3 and 4 - "Financial Mathematics I" (and "II"); the material included in these two chapters is usually covered in the first year of actuarial mathematics programmes at university.
As noted above, we think most readers will benefit from only a relatively brief study of Chapters 1 and 2, and to move onto the main chapters and start practising! It is unlikely to be beneficial to spend days memorising the material in these introductory chapters.
Most chapters are largely self-contained, with a few obvious exceptions, e.g. Financial Mathematics I and II, Contingencies I and II, the chapters on copulas, and Markov mortality models. There is a certain amount of grouping of chapters where the material is strongly related, and it is likely that most readers will tend to read a group of topics together.
A number of chapters lend themselves particularly to a relatively brief initial study, subsequently re-visiting them when studying a later chapter which uses that material. For example, application of the material in Chapters 5 and 6 is used in several later chapters of the book.
Most chapters begin with setting...
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