Problem 2: In the framework of an N-period binomial model with the parameters u, d and r consider the Asian type call option (European) which expires at N where it pays VN = max {2SN - AN, 0}. Here An is defined to be An : Sk- k=0 One can show that the arbitrage-free price of the option at n admits the representation Vn = Snfn(Xn), where fn, n = 0, 1, ..., N, are deterministic functions and Xn := An Sn 1. Write the system of recursive equations (backward induction) for the functions fn, n = 0, 1, ..., N