In the Markov model of Section 15.1, consider valuing an asset that pays an infinite stream of dividends D, where dDt Dt

= γ (Xt)dt +θ (Xt)



dBt for functions γ and θ. Assume there is no bubble. Then, the price of the asset is Pt = Et

∞

t Mu Mt Du du = DtEt

∞

t MuDu MtDt du = Dtf(Xt)

for some function f .

(a) Deduce that the rate of return is Ddt +dP P = 1 f

dt +

dD D

+

df f +

dD D

df f



.

(b) Use the result of Part

(a) to calculate the expected rate of return.

(c) Use the result of Part

(b) and the fact that the expected rate of return must equal r dt −

dM M

dP P



to derive a PDE for f .