The magazine of the Institute & Faculty of Actuaries
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Letters: Living in the real world

Andrew Cox provides an interesting analysis of curve-fitting to claims data (‘Modelling severity distributions’, December 2007). He rightly asserts that actuaries, and other financial professionals, too often fit inappropriate mathematical distributions to real-world problems. The problem of obtaining a fit to the body as well as the tail of a claims distribution is well known to actuaries, just as the problem of fitting a normal distribution to investment returns (‘fat tails’) is well-known to most investment professionals. In spite of this, the main body of investment research simply assumes that returns are normal, or log-normal, in the search for computational simplicity and mathematical evidence. I am reminded of the old adage that the difference between theory and practice is that in theory they are the same but in practice they are different. The solution that Cox recommends is to add new distributions to our toolbox and use them when appropriate. This mitigates the problem but, fundamentally, isn’t the problem more one of real-world distributions not following mathematical distributions generally? A couple of hundred years ago our forebears were attempting to fit mathematical distributions to mortality rates, and why not? If a simple mathematical formula can determine how the planets move around the sun then why wouldn’t there be a simple formula to determine something as simple as how long a person lives? As we all know, however, experience showed that this was simply not the case and the tireless efforts of actuaries over the years came up with empirically derived curves to fit mortality data, and also a new set of mathematical techniques to facilitate the use of these empirical curves. I think that actuaries should be the last people to recommend new mathematical formulae to fit empirical data; one of our greatest strengths is working with real data rather than simply assuming a normal distribution or some such in the way so many investment analysts do. Claims distributions and investment returns represent empirical data and should be analysed through empirical methods. Increasing computational power and, more importantly, the wide availability of data, have made the empirical analysis of real-world data much more practical than it was a few years ago. I believe that actuaries are well positioned to exploit this if we can see the opportunity that exists.

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