Can you please explain as much as you can. Thank you!

Textbook: Financial Mathematics A comprehensive Treatment by Giuseppe Campolieti

page 200, Exercise 5.3

21 and two Exercise 5.3. Assume a 2-by-2 economy with the state space 12 = {w',w2} and + contingent assets S1 and S, te {0,T). Assume that so > 0 and S > 0. Let S (W) - S; R for some positive constants R, i, j = 1,2. (a) Derive a simple condition (in terms of R) for the completeness of this market model ; (b) Find the risk-neutral probabilities = (wl) and 1 - = P(wa) such that the dis- counted price process is a martingale, i.e. (c) Assume that the market is complete (i.e., the condition derived in (a) holds). Find the portfolio (41,42) that replicates an arbitrary payoff X. Find the formula for to(X). ambination 21 and two Exercise 5.3. Assume a 2-by-2 economy with the state space 12 = {w',w2} and + contingent assets S1 and S, te {0,T). Assume that so > 0 and S > 0. Let S (W) - S; R for some positive constants R, i, j = 1,2. (a) Derive a simple condition (in terms of R) for the completeness of this market model ; (b) Find the risk-neutral probabilities = (wl) and 1 - = P(wa) such that the dis- counted price process is a martingale, i.e. (c) Assume that the market is complete (i.e., the condition derived in (a) holds). Find the portfolio (41,42) that replicates an arbitrary payoff X. Find the formula for to(X). ambination