The following investment is being offered on a security whose current price is s. For an initial cost of s and for the value of your choice (provided that 0

where S(1) is the price of the security at the end of one year. In other words, at the price of capping your maximum return at time 1 you are guaranteed that your return at time 1 is at least 1 + times your original payment. Show that this investment (which can be bought or sold) does not give rise to an arbitrage when K is such that

(1+)s S(1) if S(1) if (1 + )s if S(1) > K, (1+)s, S(1) return = K, (1+)s S(1) if S(1) if (1 + )s if S(1) > K, (1+)s, S(1) return = K