Set up the following problems mathematically (i.e. what equations do they satisfy and with what boundary and

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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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