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Let B(t) be 1-dimensional Brownian motion. Show that there exist 0, (t,w), 2(t, w) e W such that if we define 0 0 then V(1)

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Let B(t) be 1-dimensional Brownian motion. Show that there exist 0, (t,w), 2(t, w) e W such that if we define 0 0 then V(1) V2(1) 0 and i(t) 2 0, V2(t) 20 for a.a. t,w) Therefore both 1(t,w) and 2(t,w) are admissible portfolios for the claim F(w) -0 in the normalized market with n 1 and Xi(t)-B(t) In particular, if we drop the martingale condition in Definition 12.2.4b) we have portfolio to be admissible. (Note, however, that we have uniqueness if we require that V(0, 1), by Theorem 4.3.3) (Hint: Use Example 12.1.4 with a =-1 and with a =-2. Then define, for i 1,2, no uniqueness of replicating portfolios, even if wer equire the 0 for a-iSt

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