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I've been interested in portfolio optimization for a while now and I kind of read articles about it all over the web trying to go from the beginning (Markowitz - Merton ...), there's one thing I still can't really understand.

Here is how I see the problem : The investor has a utility function U that describes him, I guess it's inutitive to say that if we maximize the utility function for a certain trading strategy, then it would be the optimal one. So for me the intuitive task would be maximizing $E(U)$ where $E(U)$ is the expected utility.

Except that's not really how it goes. It's like each articles choses a different formula (using the utility function somewhere down the way) and say that maximizing this formula solves the portfolio optimization problem.

Like for example, last article I've been studying chose this : $E[U(V_T^{liq}(\phi))]$ where $V_T^{liq}(\phi)$ is the liquidation value of the trading strategy $\phi$ at the moment $T$.

So can anyone explain to me how the fact that there's not one "convention" isn't an issue ?

Thank you !

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    It seems like in the other example they are maximizing expected utility as well... They've just made it explicit that it's on a time horizon $T$. You have to precisely define the thing you are maximizing. From where I sit, the fact that there is no agreed upon form for the optimization target *is* an issue. In fact much research effort is devoted to scrutinizing different possible forms and investigating which make the most sense, explain anomalies the best, etc. Was that your question? – 2017-01-22
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    Yes, kind of ! Thank you for your answer. I was bothered by the fact that none of the articles I'm reading cares to give an explanation on the reason why the choose to go with one formula instead of one another. – 2017-01-22

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