Assume there is a representative investor with constant relative risk aversion . Assume aggregate consumption C satisfies

Assume there is a representative investor with constant relative risk aversion ρ. Assume aggregate consumption C satisfies dC C = α(X)dt +θ (X)



dB for functions α and θ, where X is the Markov process (13.50).

(a) Explain why the market price-dividend ratio is a function of Xt.

(b) Denote the market price-dividend ratio by f(Xt). Explain why the market risk premium is

ρθ

θ + ρθ

⎛

⎝



j=1

∂ logf(x)

∂xj

#

#

#

#

x=Xt

νj

⎞

⎠ .

How does this compare to the geometric Brownian motion model of consumption in Exercise 13.2?