Date: Nov 15, 2012 11:22 PM
Author: Paul
Subject: Linear approximation to certainty equivalent for small-valued random variable
I'm following Keeney's interpretation of risk aversion at

http://tinyurl.com/d2jskgb. For a lottery involving the addition of a

small-valued zero-mean 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?