Consider the portfolio choice problem for transaction-cost adjusted certainty equivalent maximization with risk aversion parameter γ

ω

∗

t+1 = arg max

ω∈RN ,ι′ω=1

ω

′µ − νt(ω, β) −

γ

2

ω

′Σω

where Σ and µ are (estimators of) the variance-covariance matrix of the returns and the vector of expected returns. Assume for now that transaction costs are quadratic in rebalancing and proportional to stock illiquidity such that νt (ω, B) = β
2 (ω − ωt+ )
′ B (ω − ωt+ )
where B = diag(ill1, . . . , illN )is a diagonal matrix, where ill1, . . . , illN .
Derive a closed-form solution for the mean-variance efficient portfolio ω
∗
t+1 based on the transaction cost specification above. Discuss the effect of illiquidity illi on the individual portfolio weights relative to an investor that myopically ignores transaction costs in her decision.