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Paul
Posts:
208
Registered:
2/23/10
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Linear approximation to certainty equivalent for small-valued random variable
Posted:
Nov 15, 2012 11:22 PM
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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?
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