In a market consisting of a bank account with a constant interest rate r and a non-dividend paying stock S, consider a T-claim that pays $X = S(T)/S(T_0)$ at time T, where $T_0 < T$.
a) Find a replicating strategy for X.
b) What is the arbitrage-free price of X at time 0?
Is there a name for this sort of problem, or a "general" approach that I can study? I am comfortable with replicating strategies for linear combinations, but I am not sure how to approach it with quotients and products.