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The Actuary The magazine of the Institute & Faculty of Actuaries
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On the philoparametric actuary

THE ADVANTAGES OF HAVINGONE LEG (Chesterton); Onthumbs (Montaigne); Onthe E at Delphi (Plutarch);Some thoughts on the common toad(Orwell); A meditation upon abroom-stick (Swift); Snoring for themillion (Dickens); A history of eternity(Borges); The education of anamphibian (Huxley): it is an interestingexercise to compile a list ofthe most bizarrely titled essaysbequeathed us by the greatessayists of bygone years. Inany such list, it would be hardnot to award the gold medalfor unusual titles to Thomas deQuincey’s On murder consideredas one of the fine arts.This work is as extraordinary in content as its name suggests.One of the many intriguing parts is de Quincey’saccount of how Descartes was almost murdered while ona boat journey off Germany in 1621. De Quincey tells usof the boat crew’s homicidal (and redistributist)intentions:Think, Gentlemen, of those Friezland dogs discussing aphilosopher as if he were a puncheon of rum… They madeno scruple to discuss the whole matter in his presence, asnot supposing that he understood any other language thanthat in which he conversed with his servant; and theamount of their deliberation was – to murder him, then tothrow him into the sea, and to divide his spoils.Descartes, as soon as he realised what was being discussed,‘leaped upon his feet in a trice, assumed a stern countenancethat these cravens had never looked for, and…threatened to run them through on the spot if they dared to utterhim any insult.’ He lived to cogitare another day – but it isinteresting to wonder how modern philosophy and mathematicswould have developed without the contributionof this Enlightenment pioneer.To pose that question is equivalent to asking whichamong our foibles represents an exaggeratedly rationalistEnlightenment view, and demonstrates obsessive faith inthe ability of human rationality to explain the workingsof nature. Surely one of the most guilty candidates mustbe our penchant for parametric estimation methods.Why is it that, in our search to explain random events,we are so prone to assume that the underlying process issome simple, known probability distribution? Our beliefin such underlying tidiness has always struck me as excessivelyconvenient. Indeed, one might even ascribe suchbeliefs to an overly æsthetic disposition: that it is æstheticallypreferable for observed events to be the fruit of somewell-mannered probability distribution, and for our estimationmethods to reflect such a priori preconceptions.To what extent, however, might the increased focus on‘tail estimation’ brought about by moves such as the riskbasedcapital requirements for insurers make us thinkdifferently? For instance, in his lucid article on riskquantification techniques,Mark Chaplin takes us through a numberof methods for arriving at a reasonableallowance for extreme events –and of the five methods hedescribes, two are innocently nonparametric.Non-parametric methodsare increasingly prevalent inthe actuarial syllabuses, and subject104 allows students to frolic gailywith methods such as Kaplan-Meierand Nelson-Aalen.I recently came across a particularlyinteresting example ofhow non-parametric methodscan be used in forecasting – anexample that will no doubtplease those zealots whobelieve markets to be the wisestentities of the universe. It works as follows: you wish topredict something, perhaps something qualitative (thewinner of the next Oscar for best picture), perhaps quantitative(the number of countries in the EU in 2010). Simplyconstruct a market by giving a number of players fakemoney, and allow them to trade shares in the concepts inquestion; within a few days, the total trading activity inthis market will have ended up ascribing a surprisinglyaccurate value to the object in question. One might thinkof it as a way of applying efficient market theory to theDelphi expert opinion method.This is the system underlying the Hollywood StockExchange (www.hsx.com): it has been extremely successfulin predicting, for instance, Oscar winners over the pastfew years. Virtual markets established by the University ofIowa (www.biz.uiowa.edu/iem) have proven more accuratethan have opinion polls in predicting the results of recentAmerican elections. The next time an insurer wants toestablish a reasonable 99th percentile estimate for annuallongevity improvements, or credit risk on FTSE 100 companies,all it need do is create a suitable market and let itsactuaries start to trade…Although such developments in non-parametric methodsare heartening to the empirical angel on my rightshoulder, the æsthetic, aprioristic devil lurking on my leftshoulder has not given up hope. We are all, now, consumersof stochastic processes – what the great statisticianRA Fisher once defined as ‘one bloody thing afteranother’. It is an unfortunate necessity that, to generateall those ‘bloody things’, we must generally presuppose aknown distribution. That nature imitates reason is one ofthe great conceits of modern man, and represents a reversalof medieval Scholastic thought (St Thomas Aquinascontended that reason imitates nature). Perhaps, in thefullness of time, we shall derive suitable non-parametricstochastic processes that will allow us to do our workwithout having to leave the humble portals of avowedignorance.

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