A financial model with

with two times t = 0 and t 1. Assume that there is a bank at which one can borrow or invest any amount of money between t 0 and t= 1 at the one period interest rate r> 0, where r is a constant that is known at time 0. Let us agree to say that a strategy is of type (Ar) provided that it is self-financing and the initial capital X, and terminal capital X1 satisfy (i) X1 > (1+r)X, for sure; (ii) There is a strictly positive probability that X1 > (1+r)X, Show that the model is arbitrage-free if and only if there are no strategies of type (Ar). with two times t = 0 and t 1. Assume that there is a bank at which one can borrow or invest any amount of money between t 0 and t= 1 at the one period interest rate r> 0, where r is a constant that is known at time 0. Let us agree to say that a strategy is of type (Ar) provided that it is self-financing and the initial capital X, and terminal capital X1 satisfy (i) X1 > (1+r)X, for sure; (ii) There is a strictly positive probability that X1 > (1+r)X, Show that the model is arbitrage-free if and only if there are no strategies of type (Ar)