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Proper definitions for Risk and Uncertainty (July update with (a) better notation, (b) relative risk (c) an application to insurance)

 
Paper:ewp-get/9902002
From: Thomas Cool <   > 
Date: Thu, 25 Feb 1993 20:00:16 +0100
Date (revised): Thu, 08 Jul 1999 14:10:06 -0700

Abstract:
The commonly adopted definitions of risk and uncertainty generate conceptual problems and inconsistencies, and they are a source of confusion in general. However, alternative and proper definitions are: (1) First there is the distinction between certainty and uncertainty. (2) Uncertainty forks into known (assumed) and unknown probabilities. (3) Unknown probabilities forks into known categories and unknown categories. (4) Known categories forks into 'including the uncertainties in the probabilities by explicitly assuming a uniform distribution' (Laplace) or neglect (or use other non-probabilistic techniques). Note that the term 'risk' has not been used in the 4 points above, so that an independent definition is possible. 'Risk' can be defined as the absolute value of probable loss, i.e. as rho = -E[x < 0]. Also, relative risk is the probable loss with respect to a target t, giving rho(t) = t - E[x < t]. The definitions provided here are directly in line with the Oxford English dictionary. It turns out that economics textbooks generally can keep their mathematics but will best rewrite their texts to these definitions. Not only the students and the general public will benefit from this sudden clarity, but eventually also economic theory itself. Note: This update on the February 1999 version has: (a) better notation, (b) relative risk (c) an application to insurance

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EconWPA began as a conversation between Bob Parks and Larry Blume on January 28, 1993. I located Paul Ginsparg's archive (then xxx.lanl.gov) and he graciously installed his software on a Sun Sparc system which was supporting the department of economics email and computation. EconWPA began accepting papers July 1, 1993 and had ftp, email, gopher and web interfaces. The web interface for submissions was engineered into existence in July 1995. A complete and catastrophic machine failure in 1999 caused the loss of EconWPA's email new paper announcment service at which time there were over 15,000 subscriptions with over 8,000 unique email addresses.

In 2005, Arts and Sciences commandeered the computing services that I had provided to the Department of Economics since 1987. Some might say that the department was sold out, others would (erroneously) claim that centralization is efficient, and still others would claim that I have few marketing skills.

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A Chinese curse states May you live in intersting times. I have. Bob Parks - Jan 2006