  This paper considers a utility maximization and optimal asset allocation
problem in the presence of a stochastic endowment that cannot be fully hedged
through trading in the financial market. After studying continuity properties
of the value function for general utility functions, we rely on the dynamic
programming approach to solve the optimization problem for power utility
investors including the empirically relevant and mathematically challenging
case of relative risk aversion larger than one. For this, we argue that the
value function is the unique viscosity solution of the Hamilton-Jacobi-Bellman
(HJB) equation. The homogeneity of the value function is then used to reduce
the HJB equation by one dimension, which allows us to prove that the value
function is even a classical solution thereof. Using this, an optimal strategy
is derived and its asymptotic behavior in the large wealth regime is discussed.
