"This article is simply wrong.  That probability integral looks all kinds of fancy and all, but having spent my life in finance I( have never yet known anybody who claimed to know the pdf of the returns.  I suppose that if I knew such a pdf, I would not be very interested in calculating statistics.  The Sortino ratio is a statistic and everything except the target return that goes into it is a statistic.  That DR in this vapid article is a functional of some unknown pdf which is completely useless for anything practical.  You could fix this up by making that some ""empirical pdf"" but that is pedantic and stupid.   
    

 "