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The investment economy is a main characteristic of prosperous society. Theinvestment portfolio management is a main financial problem, which has to besolved by the investment, commercial and central banks with the application ofmodern portfolio theory in the investment economy. We use the learninganalytics together with the integrative creative imperative intelligentconceptual co-lateral adaptive thinking with the purpose to advance ourscientific knowledge on the diversified investment portfolio management in thenonlinear dynamic financial system. We apply the econophysics principles andthe econometrics methods with the aim to find the solution to the problem ofthe optimal allocation of assets in the investment portfolio, using theadvanced risk management techniques with the efficient frontier modeling inagreement with the modern portfolio theory and using the stability managementtechniques with the dynamic regimes modeling on the bifurcation diagram inagreement with the dynamic chaos theory. We show that the bifurcation diagram,created with the use of the logistic function in Matlab, can provide somevaluable information on the stability of combining risky investments in theinvestment portfolio, solving the problem of optimization of assets allocationin the investment portfolio. We propose the Ledenyov investment portfoliotheorem, based on the Lyapunov stability criteria, with the aim to create theoptimized investment portfolio with the uncorrelated diversified assets, whichcan deliver the increased expected returns to the institutional and privateinvestors in the nonlinear dynamic financial system in the frames of investmenteconomy.

On the optimal allocation of assets in investment portfolio with  application of modern portfolio and nonlinear dynamic chaos theories in  investment, commercial and central banks