Paul
Posts:
517
Registered:
2/23/10


Re: Linear approximation to certainty equivalent for smallvalued random variable
Posted:
Nov 16, 2012 1:43 AM


On Nov 15, 11:22 pm, Paul <paul.domas...@gmail.com> wrote: > 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?
Correction: Pi is the risk premium for (x0 + x~), not for x~. However, the idea is the same. That is, x~ has a small value range, so (x0 + x~) does as well. Since both the mean and the certainty equivalent must occur within that small value range, the difference beween them (i.e. the risk premium) must also be small.

