The absolute risk aversion function is such that quadratic utility yields increasing absolute risk aversion.

Moreover, expected utility can be defined in terms of means and variances.

In short, it is a convenient and useful simplifying assumption.

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Dear Natale Muriana ,

I guess you're question is about $u = \mu - a\sigma^2$. I always considered this choice as a technical simplification as it represents a risk averse preferences of the investor and is at the same time easy to handle in textbook calculations (based only on the first two moments of the portfolio return distribution). So, I'm unaware that there's more behind it than mere pragmatism.

Best,

Thomas

Hello, one of the most important economic theories developed and published on behalf of the portfolio selection was to consider the magnitude of the expected risks and the return of one share until the modern theory came to diversify

An interesting question. Is the question about the investment portfolio?

The absolute risk aversion function is such that quadratic utility yields increasing absolute risk aversion.

Moreover, expected utility can be defined in terms of means and variances.

In short, it is a convenient and useful simplifying assumption.

Quadratic utility U(X)=X-aX^2 is rather simple mathematical form, that allows to use statistical methods. At the same time, it has decreasing returns to scale, or concavity. It was correctly mentioned that this function corresponds to a natural assumption of increasing absolute risk aversion. If you do not want to read books, you can read some basic information about risk aversion and utility functions here: https://en.wikipedia.org/wiki/Risk_aversion

A very good research question. There was an interesting discussion. I believe that scientific research in this area should be developed. Greetings