Assume there is a single risky asset with dividend-reinvested price S satisfying dS S = dt +

Assume there is a single risky asset with dividend-reinvested price S satisfying dS S = μdt + σ dB1 , where dμ = κ(θ −μ)dt + γ dB2 with σ, κ, θ, and γ being constants and where B1 and B2 are Brownian motions with constant correlation ρ. Assume the risk-free rate is constant. Assume an investor observes S but does not observe μ. Assume μ0 is regarded as normally distributed.

(a) Adapt the analysis of Section 23.4 to write dS/S and dμ in terms of the innovation process.

(b) Refer to Exercise 15.3 and discuss how the unobservability of μ affects the optimal portfolio of a CRRA investor.