I need detailed solution to these.

FINANCIAL CALCULUS (ii) I B = 0, and C(1,) = A(1,1)e-B(t,7), then show that A(1,7) and B(1,T) are solutions of the following ODE of boundary value problem: o(1)B(1,7) A{t,1)+((t) +a(t)b)B(t, T)A(t.T), B' (1,7) = a(t)B(t, T) -1 AT,T) = 1; B(1,1)= 0. A' (t.T) = - 2 (4) (30pts) Assume that a firm has an asset following the geometric Brownian motion V = Vidi + V.dW(), where W (1) is a standard Brownian motion under the probability measure P. As- sume there exists a money-market account with a constant riskless rater whose price is Me=e" dM= rMedt. (i) Find the asset value V4 under the risk neutral measure Q. (ii) The firm has issued a debt as a zero-coupon bond with face value D at maturity T. The payoff to debt is Br = D-max(D - V1.0). Find the value B, of the debt at time t, for 0 0 and limr-s(t.T) = 0. FINANCIAL CALCULUS (ii) I B = 0, and C(1,) = A(1,1)e-B(t,7), then show that A(1,7) and B(1,T) are solutions of the following ODE of boundary value problem: o(1)B(1,7) A{t,1)+((t) +a(t)b)B(t, T)A(t.T), B' (1,7) = a(t)B(t, T) -1 AT,T) = 1; B(1,1)= 0. A' (t.T) = - 2 (4) (30pts) Assume that a firm has an asset following the geometric Brownian motion V = Vidi + V.dW(), where W (1) is a standard Brownian motion under the probability measure P. As- sume there exists a money-market account with a constant riskless rater whose price is Me=e" dM= rMedt. (i) Find the asset value V4 under the risk neutral measure Q. (ii) The firm has issued a debt as a zero-coupon bond with face value D at maturity T. The payoff to debt is Br = D-max(D - V1.0). Find the value B, of the debt at time t, for 0 0 and limr-s(t.T) = 0