Suppose most investors have very short investing horizons and use appropriate (for them) strategies, but investor X has a very long horizon. He would like to trade some advantages (early withdrawal option, low draw-downs, etc) for the long-term return. What are theoretical approaches to model and answer this question? How should it be quantified? What are practical ways to do this?
I am not confident that I understand specifically what you are asking, but I hope this helps:
This question is rather broad. I will say that in comparing a random collection of purchases and sales of securities, with only the time between the transactions as varying among different individuals, the long-term players will have a rather substantial statistical advantage (both relative to the mean and standard deviation of returns) for 3 rather simple reasons:
This of course does not take into account your premise of over pricing of short term factors. To model such a thing would need to define your question more concisely.
Are you asking what practical ways there are of taking advantage of the fact that short term trades are overcrowded? At the risk of stating the obvious, you would need to take positions in securities which are priced on short term trends, and where those prices differ substantially from your assertion of the longer term trend price.
Since such a trend price is likely to be more strongly linked to intrinsic value of the underlying security than short term factors, you would probably do well if you could find the underlying value of the company, compare it to the current price, and purchase stock if the price undervalues the security.
This premise is underpinned by the "art" of Value Investing (see Benjamin Graham). While this method of investing by its nature tends to resist quantification, attempts have been made to quantify the process of Value Investing strategies, such as in Quantitative Value, which is an interesting read. Benjamin Graham himself employed some basic quantitative metrics for measuring the value of stocks and bonds (he quantitatively defines a Margin of Safety and also suggests an upper limit of a P/E ratio of 15 as a necessary but not sufficient condition for a stock to qualify as "cheap" and "safe" - what he would call investment grade), but at its heart the method is largely qualitative and not particularly amenable to the subject matter of this website.
I am not aware of other longer term strategies that seek long-term profits on market irrationalities specifically, but I am sure there are others out there. Value investing is probably the most logical answer to your question though, as this method - almost by its definition - seeks to capitalise on irrational short-term pricing behaviour by taking long-term positions: precisely what you were asking about.