  The investment economy is a main characteristic of prosperous society. The
investment portfolio management is a main financial problem, which has to be
solved by the investment, commercial and central banks with the application of
modern portfolio theory in the investment economy. We use the learning
analytics together with the integrative creative imperative intelligent
conceptual co-lateral adaptive thinking with the purpose to advance our
scientific knowledge on the diversified investment portfolio management in the
nonlinear dynamic financial system. We apply the econophysics principles and
the econometrics methods with the aim to find the solution to the problem of
the optimal allocation of assets in the investment portfolio, using the
advanced risk management techniques with the efficient frontier modeling in
agreement with the modern portfolio theory and using the stability management
techniques with the dynamic regimes modeling on the bifurcation diagram in
agreement with the dynamic chaos theory. We show that the bifurcation diagram,
created with the use of the logistic function in Matlab, can provide some
valuable information on the stability of combining risky investments in the
investment portfolio, solving the problem of optimization of assets allocation
in the investment portfolio. We propose the Ledenyov investment portfolio
theorem, based on the Lyapunov stability criteria, with the aim to create the
optimized investment portfolio with the uncorrelated diversified assets, which
can deliver the increased expected returns to the institutional and private
investors in the nonlinear dynamic financial system in the frames of investment
economy.
