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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

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Ken.Pledger@vuw.ac.nz

Posts: 1,383
Registered: 12/3/04
Re: Linear approximation to certainty equivalent for small-valued random variable
Posted: Nov 18, 2012 3:37 PM
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In article
<c4ea0a57-b2f4-4cad-8cd8-e606a1e57863@m4g2000yqf.googlegroups.com>,
Paul <paul.domaskis@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?



You may be lucky enough to get an answer here, but have you tried the
<alt.sci.math.probability> or <sci.stat.math> news group?

Ken Pledger.



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