Visualizing and Optimizing Portfolio with Nonlinear Transaction Costs and Specific Constraints


  • Jimbo Henri American University of Afghanistan
  • Jawad Azimi Japan International Cooperation Agency, Central Headquarter (JICA), Tokyo, Japan
  • Bianca ChenwiBianca Chenwi 3Department of Applied Mathematics, University of Bamenda, Cameroon
  • Ngongo Isidore 4Department of Applied Mathematics, University of Yaounde, Cameroon


Portfolio selection, exponential transaction cost, optimization, risk, gain, visualization.


In this paper, we consider the portfolio selection problem, with nonlinear transaction costs, basic constraints and probabilistic constraints. Such a problem cannot be handled by the usual quadratic or convex optimization methods.  We develop a heuristic method which yields to computation of efficient (suboptimal) solution of the problem. We describe our heuristic method for finding optimal portfolio based on solving many small optimization problems over large generation number, thus we obtain a good suboptimal solution.  Experimental results are demonstrated and visualized with various widely used indexes: stocks in US market: U.S. three – months treasury bills, U.S. long – term government bonds, S&P 500, Wilshire 5000, NASDAQ, Lehman Brothers corporate bond index, EAFE foreign stock index, and Gold recorded from (Jan 2000 – Jan 2008) with enhanced performance.  Finally, the results suggest that nonlinear transactions costs improve considerably the value of optimal portfolio over investment period, especially for portfolio with smaller among all assets.


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How to Cite

Henri, J., Azimi, J. ., Chenwi, B. C. ., & Isidore, N. . (2020). Visualizing and Optimizing Portfolio with Nonlinear Transaction Costs and Specific Constraints. European Journal of Applied Sciences, 7(6), 05–16. Retrieved from