  This work derives an approximate analytical single period solution of the
portfolio choice problem for the power utility function. It is possible to do
so if we consider that the asset returns follow a multivariate normal
distribution. It is shown in the literature that the log-normal distribution
seems to be a good proxy of the normal distribution in case if the standard
deviation of the last one is way smaller than its mean. So we can use this
property because this happens to be true for gross portfolio returns. In
addition, we present a different solution method that relies on the machine
learning algorithm called Gradient Descent. It is a powerful tool to solve a
wide range of problems, and it was possible to implement this approach to
portfolio selection. Besides, the paper provides a simulation study, where we
compare the derived results with the well-known solution, which uses a Taylor
series expansion of the utility function.
