Sorry if I am asking a stupid question. I refer to the ASET for this qns; since this replicating strategy is a self-financing strategy, should V(U) be equal to atAu + btBu + ctCu = X, where 0 <= t < U instead? The reason is because since it is self replicating(i.e. there is no inflow or outflow of cash to bring it up to X) then the units of A, B and C at the onset(i.e. time t) should remain the same throughout time t to time u? Appreciate any advice on my understanding. Cheers!
No, self-financing does not mean that the number of untis in the protfolio remains constant through time. In fact, we will generally need to rebalance the number of units through time so that the portfolio replicates exactly the value of the deriviative as we move through time. Self-fianancing simply means that we can rebalance the portfolio costlessly, i.e. we can change the constiuent securities without needing to spend any additional nor can we take any money out. In other words, the accumulated value of the portfolio (used to replicate the change in the derivative value over the previous dt instant of time) at the end of each previous dt instant of time is exactly to the cost of the new replicating portfolio required to replicate the derivative value over the next dt instant of time.
