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Paul
Posts:
416
Registered:
2/23/10


Linear approximation to certainty equivalent for smallvalued random variable
Posted:
Nov 15, 2012 11:22 PM


I'm following Keeney's interpretation of risk aversion at http://tinyurl.com/d2jskgb. For a lottery involving the addition of a smallvalued zeromean random variable x~ to a (presumably much larger) offset x0, the definition of risk premium (equation 4.15) is Taylor expanded (4.16 and 4.17) before dropping all terms beyond first order (4.18).
I can see why this is justified in 4.17, but I'm not 100% sure in 4.16. Usually, higher order terms are dropped when small numbers are raised to high powers. In 4.16 this case, would the reason be that pi is small? It is after all the risk premium for x~. Since x~ is very small, the expectation and the mean are small. x~ is the difference between expectation and mean, and so it must be small?



