Question: Set up the following problems mathematically (i.e. what equations do they satisfy and with what boundary and final conditions?) The assets are correlated. (a) An

Set up the following problems mathematically (i.e. what equations do they satisfy and with what boundary and final conditions?) The assets are correlated.

(a) An option that pays the positive difference between two share prices S₁ and S₂ and which expires at time T.

(b) An option that has a call payoff with underlying S₁ and strike price E at time T only if S₁ > S₂ at time T.

(c) An option that has a call payoff with underlying S₁ and strike price E₁ at time T if S₁ > S₂ at time T and a put payoff with underlying S₂ and strike price E₂ at time T if S₂ > S₁ at time T.

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