Visualizing and Optimizing Portfolio with Nonlinear Transaction Costs and Specific Constraints
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.
(1) Arnott R. D and Wagner W. H. (1990) ‘The measurement and control of trading costs’ Financial Analysts Journal. Nov/Dec: 73-80
(2) Berger A. J, Glover F. and Mulvey J. M. (1995) ‘Solving global optimization Problems in long term financial Planning’ Statistic and Operational Report Technical Report, Princeton University Press January
(3) Chang et al. (2000) ‘Heuristic and cardinality constraints Portfolio Optimizations’ Comp. Oper. Res. Vol 27, pp. 1271-1302
(4) Craven M. J. and Jimbo H.C (2013a) ‘An EA for portfolio optimization selection with multiple investment periods with exponential transaction costs’ ACM 978-1-4503-1964-5/13/07 Amsterdam, Netherlands
(5) Dantzig, G.B. and Infanger G. (1997) ‘Multistage stochastic linear programs for portfolio optimization.’ Annals of Operational Research 45:59-76
(6) Dietmar F. (2005) ‘Portfolio Management with heuristic optimization’ New York, Springer –Verlag
(7) Duan Y. C, A. (2007) ‘Mutliobjectve approach to portfolio optimization’ (online) Available at http//wwwrose-hulman/mathjournal/archives/2007/vol8-n1/paper12/v8n1-12pd.pdf.
(8) Elton E. J., Gruber M.J., Brown S. J., Brown and Goetzman W.N. (2003) ‘Modern portfolio Theory and Investment Analysis’ 6th Edition Hoboken, NJ, Wiley
(9) Elton Edwin J. (1995) ‘Portfolio Theory and Investment Analysis’ New York, Wiley
(10) Eiben A.E et al., (1994) ‘Genetic algorithm with multi-parents recombination’ Proceeding of Int. Conf. on Evolutionary computation 78-79
(11) Genott G. and Jung A. (1994) ‘Investment strategy under transaction cost. The finite horizon case’ Management Science. 40:385-404
(12) Goldberg D.E. (1989) ‘Genetic Algorithms in Search, Optimization and Machine Learning’ Addison-Westley
(13) Janikow et al., (1991) ‘An Experimental comparison of binary and floating point representation of genetic algorithm’ Proc. Of 4th Int Conf. on Genetic Algorithm: 31-36
(14) Jimbo H. C, Ouentcheu A, Bozeman R.E. (2003) ‘Portfolio optimization with the growth model’ Journal of Nonlinear and Convex Analysis, vol 6. Pp 131-141
(15) Jimbo H. C and Craven M. J. (2011) ‘Unconstrained optimization in a stochastic cellular automata system’ Journal of Nonlinear Analysis and Optimization, no1, 2: Pp 103-110
(16) Jimbo H.C and Craven M.C. (2013b) ‘Optimization of stock investment portfolio with stochastic constraints’ Journal of Nonlinear and Convex Analysis – I, Yokohama Published Pp 127 – 143
(17) Kanski, J.J., Andrzej D. (2002) ‘Evolutionary algorithms for single and multicriteria design optimization, Heidelberg’ Germany: Physica – Verlag
(18) Loeb T. F. (1993) ‘Trading costs: The critical link between investment and information and results’ Financial Analysts Journal. May/June: 39-44
(19) Murtagh B. A. and Saunder M. (1978) ‘Mathematical Programming’ 14:41-72
(20) Mulvey J.M. Incorporating transaction costs in models for assets allocations: (1993) Financial Optimization. Stavros A. Zenios, Cambridge University Press
(21) Perold A. F. (1984) ‘Large Scale Portfolio Optimization’ Management Science. 30:1143-1160
(22) Ting Chuan-Kang (2005) ‘On the mean convergence time of multi-parents genetic algorithm without selections’ Advances in Artificial Life 403 – 412
(23)Liang, Z., et al., The detection and quantification of retinopathy using digital angiograms. Medical Imaging, IEEE Transactions on, 1994. 13(4): p. 619-626.
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