2) We consider the following two one time period market models on the finite proba- bility space N = {w1, W2, W3} mit P(Wi) > 0 (i = 1, 2, 3) i) The model consists of four assets whose prices at time 0 and 1 are given as follows 5o = (SO, S., S2, S3) = (1, 7, 31, 62), SO = 2, S}(wi) Si(wi) S}(wi) | / 40 60 120 Sl(w2) S (W2) Silw2)= 0 40 80 | Si(w3) S (w3) Silw3) ) ( 20 100 200 ) ii) 5o = (S, S5, S3) = (1,8, 10), S= 1, | Si(wi) S (wi) 1 / 6 11 S](w2) S(wa) = ( 5 11 S}(w3) S (3) / ( 129 ) Are these models arbitrage-free? If yes, specify all risk-neutral measures, and if not, give an arbitrage strategy. Hint: In a one period market model a probability measure Q is a martingale or risk-neutral measure if the expectation Eo ] = S, for all i = 1, ...,d. 2) We consider the following two one time period market models on the finite proba- bility space N = {w1, W2, W3} mit P(Wi) > 0 (i = 1, 2, 3) i) The model consists of four assets whose prices at time 0 and 1 are given as follows 5o = (SO, S., S2, S3) = (1, 7, 31, 62), SO = 2, S}(wi) Si(wi) S}(wi) | / 40 60 120 Sl(w2) S (W2) Silw2)= 0 40 80 | Si(w3) S (w3) Silw3) ) ( 20 100 200 ) ii) 5o = (S, S5, S3) = (1,8, 10), S= 1, | Si(wi) S (wi) 1 / 6 11 S](w2) S(wa) = ( 5 11 S}(w3) S (3) / ( 129 ) Are these models arbitrage-free? If yes, specify all risk-neutral measures, and if not, give an arbitrage strategy. Hint: In a one period market model a probability measure Q is a martingale or risk-neutral measure if the expectation Eo ] = S, for all i = 1, ...,d