Exercise 15 Consider a one-period financial market model that consists of the risk-free asset and a risky asset, defined on the probability space (,F,P), where :={1,2,3},F:=2 and pi:=P({i})>0 for every i=1,2,3. Assume that r=0, i.e. S00=S10=1, while the risky asset satisfies S0=1 and S1(1)=21,S1(2)=1,S1(3)=25. (i) Describe the set of equivalent martingale measures as a subset of R3. (ii) Consider the claim C with payoff C(1)=3,C(2)=6,C(3)=3. Compute the sub- and super-replication prices (C) and (C). (iii) Consider another claim C with payoff C(1)=c1,C(2)=c2,C(3)=c3. Find a condition on c1,c2,c3 such that the claim C is replicable via S:=(S0,S)