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On the Methodology of Actuarial Science Some Notes on the Methodology of Actuarial Science Copyright Craig Turnbull FIA Edinburgh, UK. 7th April 2020. Table of Contents Introduction ........................................................................................................................................ 4 Part One: Probability and Methodology in Science ............................................................................ 6 1. Philosophical theories of probability .......................................................................................... 7 1.1 Theories of objective probability ........................................................................................ 8 1.2 Theories of subjective probability ..................................................................................... 15 1.3 Induction and the logical approach to probability ............................................................ 24 1.4 Some final thoughts .......................................................................................................... 34 2. Probability and methodology in the natural sciences .............................................................. 37 2.1 Falsificationism – an objectivist’s approach to scientific inference .................................. 39 2.2 Bayesianism - an epistemological alternative ................................................................... 49 2.3 Causation and scientific explanation ................................................................................ 56 2.4 Realism and instrumentalism............................................................................................ 64 2.5 Post-positivism .................................................................................................................. 66 3. On the methodology of the social sciences .............................................................................. 72 3.1 History as a form of scientific explanation ........................................................................ 73 3.2 Positivism in the social sciences ........................................................................................ 79 3.3 Interpretivism.................................................................................................................... 89 4. On the methodology of economics........................................................................................... 95 4.1 Economics as a positive social science .............................................................................. 95 4.2 Beyond positivism….an interpretivist perspective on economics .................................. 111 4.3 Econometrics and macroeconomics ............................................................................... 116 Part Two: On the Methodology of Actuarial Science ...................................................................... 122 5 Contemporary methodology of actuarial science .................................................................. 123 5.1 A brief history of thought on the methodology of actuarial science .............................. 123 5.2 General characteristics of actuarial science as a scientific discipline ............................. 126 5.3 Some key methodological considerations that arise ...................................................... 132 5.4 Localism and the prospects of predictive success in actuarial modelling ...................... 133 5.5 Model risk and uncertainty ............................................................................................. 143 5.6 Economic theory and actuarial science .......................................................................... 150 5.7 Professional judgement and modelling skill ................................................................... 153 6 Implications for an improved actuarial methodology ............................................................ 157 6.1 Risk appetite in actuarial financial institutions ............................................................... 157 6.2 Risk and capital measurement ........................................................................................ 165 6.3 Data science and actuarial science ................................................................................. 175 Appendix – The historical development of economics ................................................................... 187 Bibliography .................................................................................................................................... 194 Introduction “Philosophy, though unable to tell us with certainty what is the true answer to the doubts which it raises, is able to suggest many possibilities which enlarge our thoughts and free them from the tyranny of custom.” Bertrand Russell, The Problems of Philosophy, 1912. This famous Bertrand Russell quotation is representative of the spirit with which this work has been undertaken. This work aims to consider the methodology of actuarial science through the lens of the philosophy of science. In doing so, few ‘true answers’ will be irrefutably established. But I hope the work can offer some observations and suggest some possibilities that stimulate actuaries to consider different approaches to actuarial science and modelling. The following pages seek to step back from our day-to-day actuarial methods by questioning the robustness of their premises and logic, identifying their implied limits, and speculating on where alternative methods may offer greater prospects of success (and, indeed, sometimes re-considering what actuarial success might look like). Over the course of the work some specific and detailed answers to the methodological questions raised will be offered. But these answers can only be regarded as tentative and fallible opinions, rather than claims to truth. In the spirit of Russell above, the value of the work is not necessarily found in determining the right answers, but in demonstrating the benefit of asking the questions. I hope these pages stimulate more actuaries to ask these methodological questions and share their own tentative answers. Relatively little of this type of study has been published by actuaries, especially in the 21st century. The experience of undertaking this study allows me to testify to some of the good reasons for that. The process necessarily involves considering professional practice areas outside the methodologist’s own specific area of expertise and offering some constructive but contentious advice. It requires a willingness to stick one’s head above the parapet far enough to scan the horizon without worrying too much about being shot in the eye. This leads me to vouch for another quotation, this time from a methodologist in economics: “The study of methodology is an agonizing task; writing a book on the subject requires the skills of an individual who is at once presumptuous and masochistic.”1 In truth, undertaking this work has been far from agony…in fact, this has been the most stimulating and enjoyable body of actuarial study that I have ever undertaken. But I often identified with the purported character traits. The Structure of this Work and How to Read It So, the following chapters are intended to free our actuarial minds from the tyranny of custom by examining the doubts raised by a philosophically-minded review of the methodology of actuarial science. This is performed in two stages. First, Part One provides an overview and discussion of some of the key areas of the philosophy of science that might be relevant to the methodology of actuarial science. Little of this discussion is specific to actuarial science, but it is written with actuarial contexts in mind where possible. Part Two then seeks to apply the ideas and insights developed in Part One to the specifics of actuarial science and its methodology. 1 Caldwell (1994), p. 1. Part One is quite long and some of it is doubtless less than strictly relevant to actuarial science. The less philosophically curious or, indeed, the already philosophically well-read reader may choose to regard Part One as a sort of extended appendix - and thereby avoid reading it except where Part Two suggests it is useful. These readers can skip straight on to Part Two, which has been written with this approach in mind, and which therefore has frequent referencing and signposting of the relevant Part One material. Part One: Probability and Methodology in Science 1. Philosophical theories of probability What do we mean by the word ‘probability’? At first sight, the answer may appear so intuitive and obvious as to make the question seem frivolous. Isn’t it merely the likelihood of some well-defined event happening over some well-defined time interval or amongst some specified number of instances? And didn’t the great Pierre Simon Laplace adequately address the question 200 years ago in the very first sentence of his treatment of probability: “The probability for an event is the ratio of the number of cases favourable to it, to the number of all cases possible when nothing leads us to expect that any one of these cases should occur more than any other, which renders them, for us, equally possible.”2 By the end of this chapter the reader may have a fuller appreciation of the different interpretations that can be placed on Laplace’s definition. These alternative interpretations will demonstrate that the word ‘probability’ can mean surprisingly different things to different people. This is, in part, simply a consequence of the
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