(1) Advance math level including probabilitty theory (2) Graduate course in portfolio optimization (3) Actual experience apllying math models and optimization These are the assumptions. Are you expecting anyone who spent his youth studying for a degree in finance to explain them to you in a few lines in a forum?
lol! Let us start with something easier. Do you know what assumptions are required to justify the statement 1+1 = 2?
I believe that it took something like 200 pages of formal proofs for Russell to prove that in Principia Mathematica http://en.wikipedia.org/wiki/Principia_Mathematica#Quotations
And of course Principia was washed away not long after http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf