Paul
Posts:
208
Registered:
2/23/10
|
|
Re: Linear approximation to certainty equivalent for small-valued
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 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?
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.
|
|
