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Topic: Linear approximation to certainty equivalent for small-valued random variable
Replies: 3   Last Post: Nov 21, 2012 5:21 PM

 Messages: [ Previous | Next ]
 Paul Posts: 517 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.

Date Subject Author
11/15/12 Paul
11/16/12 Paul
11/18/12 Ken.Pledger@vuw.ac.nz
11/21/12 Paul