Consider the following probability space (2,F,P): = {w, wz, w3}, F = 2 and P[{w}]>0 for...

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Consider the following probability space (2,F,P): = {w₁, wz, w3}, F = 2 and P[{w}]>0 for i = 1,2,3. Suppose r> -1 and -1 < d <m<u are given constants. Consider a market 5 = (S0, S¹) defined by S= 1, S > 0, S(w) = 1+r. S(w) = S/{1+ dl {₁} (w) + ml {₂} (w) + ul{₂} (w)}, for le), bent well 7 pts (a) For which values of r the market 5 does not admit arbitrage opportunities? (b) Suppose that 5 is arbitrage-free. Does there exist a trading strategy such that 0.5₁ = (SK)+ P-a.s., where K> 0 is an arbitrary (but fixed) strike price? If it does, prove (or disprove) its uniqueness and calculate the initial cost - So. 8 pts (c) How do your answers to (a) and (b) change in the following three scenarios: one of P[{w}] is equal to zero, i = 1,2,3? 10 pts Consider the following probability space (2,F,P): = {w₁, wz, w3}, F = 2 and P[{w}]>0 for i = 1,2,3. Suppose r> -1 and -1 < d <m<u are given constants. Consider a market 5 = (S0, S¹) defined by S= 1, S > 0, S(w) = 1+r. S(w) = S/{1+ dl {₁} (w) + ml {₂} (w) + ul{₂} (w)}, for le), bent well 7 pts (a) For which values of r the market 5 does not admit arbitrage opportunities? (b) Suppose that 5 is arbitrage-free. Does there exist a trading strategy such that 0.5₁ = (SK)+ P-a.s., where K> 0 is an arbitrary (but fixed) strike price? If it does, prove (or disprove) its uniqueness and calculate the initial cost - So. 8 pts (c) How do your answers to (a) and (b) change in the following three scenarios: one of P[{w}] is equal to zero, i = 1,2,3? 10 pts

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