Exercise 2 (15 points): Consider the following boundary value problem: t OF (t, x) + %...

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Exercise 2 (15 points): Consider the following boundary value problem: t OF (t, x) + % ! OF 2 (t, x) + (t, x) = F (t, x) F(2,x)=1{x>50}, Solve for F (0, 40), using the Feyman-Kac Theorem. Note: F (2,x) can be interpreted here as the payoff of a digital option maturing in T = 2 years. Moreover, for any random variable Z and tR, E 1{z>}] = P[Z > t]. Exercise 2 (15 points): Consider the following boundary value problem: t OF (t, x) + % ! OF 2 (t, x) + (t, x) = F (t, x) F(2,x)=1{x>50}, Solve for F (0, 40), using the Feyman-Kac Theorem. Note: F (2,x) can be interpreted here as the payoff of a digital option maturing in T = 2 years. Moreover, for any random variable Z and tR, E 1{z>}] = P[Z > t].