PORTFOLIO OPTIMIZATION ALGORITHMS
Keywords:
portfolio, optimization, algorithms.Abstract
A milestone in Portfolio Theory is represented by the Mean-Variance Model introduced in 1952 by Harry Markowitz. During the years, mathematicians have developed several different models extending, improving and diversifying the Mean-Variance Model. This paper will briefly present some of these extensions and the resulted models. The aim is to search and identify some connections between portfolio theory and energy production. Analyzing the Mean-Variance Model and its extensions we can conclude that from practical point of view the minimax model is the easiest to be implemented, because the analytical solution is computed with low effort. This model, like all others from Portfolio Theory, has a high sensitivity for mean. We consider that this model fits to our goal (energy optimization) and we intend to implement it in our future research project.
References
Amihud Y., Mendelson H., Liquidity and Asset Prices: Financial Management Implications, Financial Management, vol. 17, no. 1, 1988, pp. 5-15
Bellman R.E., Dreyfuss S.E., Programare dinamica aplicata, Editura Tehnica Bucuresti, 1967
Best M.J., Grauer R.R., Sensitivity Analysis for Mean-Variance Portfolio Problems, Management Science, vol. 37, no. 8, 1991, pp. 980-989
Best M.J., Grauer R.R., On the Sensitivity of Mean-Variance Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results, The Review of Financial studies, vol. 4, no. 2, 1991, 315-342
Cai X., Teo K-L.,Yang X., Zhou X.Y. Portofolio optimization under a minimax rule, Management Science, vol. 46, no. 7, July 2000, pp. 957-972
Chopra V.K., Hensel C.R., Turner A.L., Massaging Mean-variance Inputs: Returns from Alternative Global Investment Strategies in the 1980s, Management Science, vol. 39, no. 7, 1993, pp. 845-855
Constantinides G.M., Capital Market Equilibrium with Transactions Costs, Journal of Political Economy, vol. 94, no. 4, 1986, pp. 842-862
Dumas B., Luciano E., An Exact Solution to a Dynamic Portfolio Choice Problem under Transaction Costs, Journal of Finance vol. 46, no. 2, 1991, pp. 577-595
Elton E.J., Gruber M.J., The Multi-Period Consumption Investment Problem and Single period Analysis, Oxford Economic Papers, vol. 26, no. 2, 1974, pp. 289-301
Elton E.J., Gruber M.J., On the Optimality of Some Multiperiod Portfolio Selection Criteria, The Journal of Business, vol. 47, no.2, 1974, pp. 231-243
Fama E.F., Multiperiod Consumption-Investment Decision, American Economic Review, vol. 60, no. 1, 1970, pp. 163-174
Francis J.C., Investment: Analysis and Management, McGraw-Hill, New York, 1976
Grauer R.R., Hakansson N.H., On the Use of Mean Variance and Quadratic Approximations in Implementing Dynamic Investment Strategies: A Comparison of Returns and Investment Policies, Management Science, vol. 39, no. 7, 1993, pp. 856-871
Hakansson N.H., Multi-Period Mean Variance Analysis: Toward a General Theory of Portfolio Choice, Journal of Finance, vol. 26, no. 4, 1971, pp. 857-884
Huang X., Qiao L., A risk index model for multi-period uncertain portfolio selection, Information Science, vol 217, 2012, pp. 108-116
Karacabey A.A., Risk and investment opportunities in portofolio optimization, European Journal of Finance and Banking Research, vol. 1, no. 1, 2007, pp. 1-15
Konno H., Portfolio optimization using L1 risk function, IHSS Report 88-9, Institute of Human and Social Sciences, Tokyo Institute of Technology, 1988
Konno H., Yamazaki H., Mean absolute deviation portofolio optimization model and its applications to Tokyo Stock Market, Management Science, vol. 37, no. 5, May 1991, pp. 519-531
Lee C.F., Finnerty J.E., Wort D.H., Index Models for Portfolios Selection, Handbook of Quantitative Finance and Risk management, 2010, pp. 111-124
Li D., Ng W.L., Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation, Mathematical Finance, vol. 10, no. 3, July 2000, pp. 387-406
Markowitz H., Portofolio Selection, The Journal of Finance, vol. 7, no. 1, March 1952, pp. 77-91
Merton R.C., Lifetime Portfolio Selection under Uncertainity: The continuous time case, Review of Economics and Statistics, vol. 51, no. 3, 1969, pp. 247-257
Merton R.C., An Analytic derivation of the Efficient Portfolio Frontier, Journal of Financial and Quantitative Analysis, vol. 7, no. 4, 1972, pp. 1851-1872
Merton R.C., Continuous Time Finance, Blackwell Cambridge, 1990
Mossin J., Optimal Multiperiod Portfolio Policies, Journal of Business, vol 41, no.2, 1968, pp. 215-229
Perold A.F., Large Scale Portfolio Optimization, Management Science, vol. 30, 1984, pp 1143-1160
Perold A.F., The implementation shortfall: Paper versus reality, The Journal of Portfolio Management, vol. 14, no. 3, 1988, pp. 4-9
Rubinstein M, Markowitz’s “Portfolio Selection”: A Fifty-Year Retrospective, Journal of Finance, vol. 57, no. 3, 2002, pp. 1041-1045.
Samuelson P.A., Lifetime Portfolio Selection by Dynamic Stochastic Programming, Review of Economics and Statistics, vol. 51, no. 3, 1969, pp. 239-246
Sharpe W., A Simplified Model for Portfolio Analysis, Management Science, vol. 9, no. 2, 1963, pp. 277-293
Sharpe W., A Linear Programming Algorithm for a Mutual Fund Portfolio Selection, Management Science, vol 13, no. 7, 1967, pp. 499-510
Sharpe W., A Linear Programming Approximation for General Portfolio Selection Problem, Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6, no. 5, 1971, pp. 1263-1275
Smith K.V., A Transition Model for Portfolio Revision, Journal of Finance, vol. 22, no.3, 1967, pp. 425-439
Stone B.K., A Linear Programming Formulation of the General Portfolio Selection Problem, Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8, no. 4, 1973, pp. 621-636
Von Hohenbalker B., A Finite Algorithm to maximize Certain PseudoConcave Functions on Polytopes, Mathematical programming, vol. 9, no. 1, 1975, pp. 189-206
Winklwer R., Barry C.B., A bayesian model for portfolio selection and revision, Journal of Finance, vol. 30, 1975, pp. 179-192
Young R., A Minimax Portfolio Selection Rule with Linear Programming Solution, Management Science, vol.44, no. 5, 1998, pp. 673-683
Yu M., Takahashi S., Inoue H., Wang S., Dynamic portofolio optimization with risk control for absolute deviation model, European Journal of Operational Research, vol. 201, no. 2, 2010, pp. 349-364
Yu M., Wang S., Dynamic optimal portofolio with maximum absolute deviation model, Journal of Global Optimization, vol 53, 2012, pp. 363-380
Yu M., Wang S., Lai K., Chao X., Multiperiod portfolio selection on a minimax rule, Dynamics of Continuous, Discrete and Impulsive Systems, Serie B: Applications and Algorithms, no. 12, 2005, pp. 565-587.
Yu P.L., Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives, Journal of Optimization Theory and Applications, vol. 14, no. 3, 1974, pp. 319-377
Zidaroiu C., Programare dinamica discreta, Editura Tehnica Bucuresti, 1975
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