  In this paper, we explore the portfolio allocation problem involving an
uncertain covariance matrix. We calculate the expected value of the Constant
Absolute Risk Aversion (CARA) utility function, marginalized over a
distribution of covariance matrices. We show that marginalization introduces a
logarithmic dependence on risk, as opposed to the linear dependence assumed in
the mean-variance approach. Additionally, it leads to a decrease in the
allocation level for higher uncertainties. Our proposed method extends the
mean-variance approach by considering the uncertainty associated with future
covariance matrices and expected returns, which is important for practical
applications.
