Simplicity!
Under the risk neutral measure, the market price of risk {[Mu-r]/sig} is 0. So Mu = r. So if St ~ LogNor( ln(S0) + (r - sig^2/2)*t, sig*dt). So, the discounted expected value of the stock process under risk free measure is a martingale - and the portfolio can be replicated - bam!
If you're assuming a risk lover, he will have a negative MPR. Mu = r - sig*MPR. Discounted value of this process under r is NOT a martingale - so you'll need to find something else to discount it with. This will vary for each instrument and person, and will be impossible to strike a balance ... and all this makes things more complicated.
Additionally, risk neutral measure theoretical sense too - given you'll have risk lovers and risk averse people sort of evenly distributed, with a mean risk taking ability of 0 at a portfolio level...
Last edited: Aug 15, 2013