Risk: Mathematical and Otherwise

Abstract

In 1999 NASA's Mars Climate Orbiter burned and crashed because no one had thought to check whether force, expressed in pounds, had been converted to force expressed in Newtons (Grossman, 2010). Failure to carry the one, or convert pounds to Newtons, are examples of only one of the risks encountered in attempting to apply mathematics to the management of risk.Assuming they can remember to carry the one, what role might mathematicians have to play in the management of risk? The idea of turning a risk, a possibility of loss or injury, into a "calculated" risk, a quantified probability of loss or injury, is one that has obvious appeal not just to statisticians and mathematicians - but to large numbers of others who would like to know the probability of failure before pursuing some intended course of action."Risk" (almost a billion Google hits) has become a booming business. "Risk management" yields over 80 million hits, and "chief risk officer" (of interest to those looking for employment in this field) returns half a million. Governments are keen on risk management: Turnbull, Basel, Sarbanes-Oxley are names associated with guidance, accords or legislative acts intended to ensure that financial risks are managed effectively. Most big banks now have extraordinarily highly paid chief risk officers (CROs) to ensure compliance with their requirements - in 2011 the CRO at Bank of America was paid $11.4 million (Bloomberg News, 2011). Other large, non-financial, enterprises such as General Motors and Ford, Shell and BP, Delta Airlines, Toyota, also have senior executives bearing the CRO title.The financial meltdown of 2007/2008 gave a huge boost to the risk management industry. It has now declared itself a profession and it is growing at an impressive rate: GARP, the Global Association of Risk Professionals grew more than three-fold from 55,000 members pre-crash in 2006 to more than 175,000 by 2011.Types of RiskThe growing army of risk managers seeks to manage an extraordinary range of different risks. Here is a short starter list: financial risk (credit risk, market risk, liquidity risk, value at risk ...), legal risk, reputation risk, medical risk, strategic risk, policy risks, inflation risk, recession risk, terrorism risk, sanctions risk, climate risk, radiation risk, extreme weather risk, road accident risk, etc., etc.The list could go on almost without end. Any threat of nature or any human activity, physical or intellectual, leading to an uncertain outcome can serve as a descriptor of a type of risk.A further, less open-ended, set of categories can be helpful in an attempt to illuminate the challenges facing risk managers seeking to reduce risks to calculable probabilities. Figure 1 presents a risk typology that is germane to most discussions of a wide variety of risks and their management.The Venn diagram in Figure 1 suggests that the typology can be useful to distinguish three different, but not mutually exclusive, types of risk. One need sample only a tiny fraction of the 100s of millions of Google "risk" hits to discover unnecessary and often acrimonious arguments caused by people using the same word to refer to different things and shouting past each other. The typology offered in Figure 1 can help to dispose of some unnecessary arguments and, perhaps, civilize others.Risks in the perceived directly circle are managed using judgement. We do not undertake a formal, probabilistic risk assessment before crossing the road; some combination of instinct, intuition and experience usually sees us safely to the other side. The consequences of failing to carry the one, or convert pounds to Newtons are, like road accidents, usually the result of carelessness: a failure pay attention to directly perceptible hazards.The second, the risk-perceived-through-science circle, dominates the risk management literature. This is the circle within which most of the risk professionals ply their trade. …