  Optimal portfolio selection problems are determined by the (unknown)
parameters of the data generating process. If an investor wants to realise the
position suggested by the optimal portfolios, he/she needs to estimate the
unknown parameters and to account for the parameter uncertainty in the decision
process. Most often, the parameters of interest are the population mean vector
and the population covariance matrix of the asset return distribution. In this
paper, we characterise the exact sampling distribution of the estimated optimal
portfolio weights and their characteristics. This is done by deriving their
sampling distribution by its stochastic representation. This approach possesses
several advantages, {e.g.} (i) it determines the sampling distribution of the
estimated optimal portfolio weights by expressions, which could be used to draw
samples from this distribution efficiently; (ii) the application of the derived
stochastic representation provides an easy way to obtain the asymptotic
approximation of the sampling distribution. The later property is used to show
that the high-dimensional asymptotic distribution of optimal portfolio weights
is a multivariate normal and to determine its parameters. Moreover, a
consistent estimator of optimal portfolio weights and their characteristics is
derived under the high-dimensional settings. Via an extensive simulation study,
we investigate the finite-sample performance of the derived asymptotic
approximation and study its robustness to the violation of the model
assumptions used in the derivation of the theoretical results.
