Comparison of the risk-sensitive value measure and mean-variance approach under normal mixture

Year：2017 NO： Author：Jiro Hodoshima, Tetsuya Misawa, Yoshio Miyahara

We study an expected exponential utility function approach in order to measure a random cash flow $\mb.$
The utility indifference price of the random cash flow $\mb$ is a measure of value defined to be given by
the solution $\nu$ of the equation $E[u(- \nu + \mb)] = 0$ where $u(\cdot)$ is a non-decreasing
utility function and $E$ denotes expectation.
We evaluate the utility indifference price when $u(x) = \frac(1 - e^)$ where $\alpha > 0,$
which we call the risk-sensitive value measure, under the flexible class of normal mixture distributions.
It has desirable properties as a value measure.
We compare the risk-sensitive value measure and mean-variance approach
under normal mixture distributions and provide an empirical application.

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