  In this paper we propose and analyze a method based on the Riccati
transformation for solving the evolutionary Hamilton-Jacobi-Bellman equation
arising from the stochastic dynamic optimal allocation problem. We show how the
fully nonlinear Hamilton-Jacobi-Bellman equation can be transformed into a
quasi-linear parabolic equation whose diffusion function is obtained as the
value function of certain parametric convex optimization problem. Although the
diffusion function need not be sufficiently smooth, we are able to prove
existence, uniqueness and derive useful bounds of classical H\"older smooth
solutions. We furthermore construct a fully implicit iterative numerical scheme
based on finite volume approximation of the governing equation. A numerical
solution is compared to a semi-explicit traveling wave solution by means of the
convergence ratio of the method. We compute optimal strategies for a portfolio
investment problem motivated by the German DAX 30 Index as an example of
application of the method.
