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Show that: a) The price of the stock itself, that is whenu(t,X t ) =X t , solves the Black-Scholes-Merton partial differential equation; b) The

Show that:

a) The price of the stock itself, that is whenu(t,X_t) =X_t, solves the Black-Scholes-Merton

partial differential equation;

b) The risk-free interest rate r compounded continuously solves the Black-Scholes PDE, that is

whenu(t, X_t) =e^rt.

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