“…Hence, the portfolio of an investor consists of static positions in the call options in addition to the usual dynamically updated risky asset. This leads us to a similar structure to that in [19] and in other papers [6,8,10,11,14,15,18,21,22,23,24,25,29] which consider modelindependent pricing. This approach is very closely related to path-wise proofs of well-known probabilistic inequalities [2,9].…”