# Which is the better risk sensitive measure?

Consider the two following optimization problem

1) $$\min_{\theta} \ln E_{\theta}[ e^{X}]$$

2) $$\min_{\theta} E_{\theta}[ X]$$ with the constraint $$Var_{\theta}[X] <c$$

Is it true that the first one is a better measure for risk-sensitivity cost as it takes other moments (which is visible from the Taylor series expansion) also into account ?

In general, can we say anything about the usefulness of the first cost compared to any other risk-sensitive cost ?

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What is $\theta$? A probability measure? If so, from which set of measures? $Var$ is variance or value-at-risk? Where do you take these definitions from? – Richard Nov 12 '14 at 9:39