بهينه سازي پورتفوليو با رويکرد متغيرهاي تصادفي فازي
الموضوعات :
1 - تربیت مدرس
الکلمات المفتاحية: انتخاب پورتفوليو - برنامه ريزي فازي- برنامه ريزي غير خطي عدد صحيح – الگوريتم هيبريدي,
ملخص المقالة :
يکي از زمينه هايي که تحقيقات بسياري در حوزه آن صورت گرفته است مسايل مالي و بخصوص پورتفوليو مي باشد. هدف اين تحقيق بهينه سازي انتخاب پورتفوليو بگونه اي است که نه تنها با شرايط محيطي انطباق بيشتري داشته باشد، بلکه به نتايج بهتري نسبت به متدهاي قبل دست يابد. در اين تحقيق مساله انتخاب پورتفوليو با بازگشت سرمايه اي که بصورت متغيرهاي تصادفي فازي مي باشد بررسي مي گردد. چون حل چنين مدلهايي با روشهاي سنتي ميسر نمي باشد، لذا يک الگوريتم هيبريدي براي حل مساله ارائه شده است. براي اجراي روش هيبريدي ابتدا با استفاده از شبکه هاي عصبي فازي جواب موجه اوليه بدست آمده و سپس با رويکرد الگوريتم ژنتيک جواب بهينه محاسبه گرديد.
المصادر:
- Abdelaziz, F.B., Lang, P., Nadeau, R. (1999). Efficiency in multiple criteria under uncertainty, Theory and Decision 47, 191–211.
- Abdelaziz, F.B., Mejri, S. (2001). Application of goal programming in a multi-objective reservoir operation model in Tunisia, European Journal of Operational Research 133, 352–361.
- Ammar, E. E. (2007). On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem, Information Sciences, Available Online 4 April.
- Aouni, B., Ben Abdelaziz, F., Martel, J. M. (2005). Decision-maker’s preferences modeling in the stochastic goal programming, European Journal of Operational Research 162, 610–618.
- Bawa, V.S., Lindenberg, E.B. (1977). Capital market equilibrium in a mean-lower partial moment framework, Journal of Financial Economics 5, 189–200.
- Campbell, J.Y., Lo, A.W., Mac Kinlay, A.C. (1997). The Econometrics of Finance Markets, Princeton University Press, Princeton, NJ.
- Carlsson, C., Fullér, R. (2001). On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122, 315–326.
- Chow. K., Denning. K. C., (1994). On variance and lower partial moment betas: the equivalence of systematic risk measures, Journal of Business Finance and Accounting 21, 231–241.
- Ehrgott, M., Klamroth, K., Schwehm, C. (2004). An MCDM approach to portfolio optimization, European Journal of Operational Research. 155, 752–770.
- Elton, E.J., Gruber, M.J. (1995). Modern Portfolio Theory and Investment Analysis, Wiley, New York.
- Glickman.T. S. (2008). Program portfolio selection for reducing prioritized securities, European Journal of Operational Research 190, 268–276.
- Gupta, P; Mehlawat, M. K; Saxena, A. (2008). Asset portfolio optimization using fuzzy mathematical programming. Information Sciences 178, 1734-1755.
- Hasuike, T., Katagiri, H., Ishii, H. (2009). Portfolio selection problems with random fuzzy variable returns. Fuzzy Sets and Systems. ARTICLE IN PRESS.
- Holland, J. Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, 1975.
- Huang, X. (2006). Fuzzy chance-constrained portfolio selection, Applied Mathematics and Computation 177, 500–507.
- Huang, X. (2007, a). Two new models for portfolio selection with stochastic returns taking fuzzy information, European Journal of Operational Research 180, 396–405.
- Huang, X. (2007, b). A new perspective for optimal portfolio selection with random fuzzy returns, Journal of Information Sciences 177, 5404–5414.
- Inuiguchi, M., Ramik, J. (2000). Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem, Fuzzy Sets and Systems 111, 3–28.
- Jorion, P. (1992). Portfolio optimization in practice, Financial Analysis Journal January–February 68–74.
- Katagiri, H., Ishii, H., Sakawa, M. (2004). On fuzzy random linear knapsack problems, Central European Journal of Operations Research 12, 59–70.
- Korner, R. (1997). On the variance of fuzzy random variables. Fuzzy Sets and Systems, 92, 83−93.
- Kruse R, and Meyer KD, Statistics with Vague Data, D. Reidel Publishing Company, Dordrecht, 1987.
- Kumar, P.C., Philippatos, G. C., Ezzell, J.R. (1978). Goal programming and the selection o portfolios by dual-purpose funds, The Journal of Finance 33, 303–310.
- Kwakernaak, H. K. (1978). Fuzzy random variables-I, Information Sciences 15, 1–29
- Kwakernaak, H.K. (1979). Fuzzy random variables-II, Information Sciences 17, 153–178
- Lacagnina, V., Pecorella, A. (2006). A stochastic soft constraints fuzzy model for a portfolio selection problem, Fuzzy Sets and Systems 157, 1317 – 1327.
- Lai, Y.J., Hwang, Ch. L. (1992). Fuzzy mathematical programming. Methods and applications. Springer-Verlag. Berlin, pp 257-270.
- Lee, S.M., Chesser, D. L. (1980). Goal programming for portfolio selection, The Journal of Portfolio Management 22–26.
- Leon, R.T., Liern, V., Vercher, E. (2002). Validity of infeasible portfolio selection problems: fuzzy approach, European Journal of Operational Researches 139, 178–189.
- Lin, Ch., Hsieh, P. J, (2004). A fuzzy decision support system for strategic portfolio management, Decision Support Systems, 38, 383-398
- Lintner, B. J. (1965). Valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics 47, 13–37.
- Liu, B. (2001). Fuzzy random chance-constrained programming, IEEE Transactions on Fuzzy Systems, Vol. 9, No. 5, 713-720.
- Liu, B. (2002). Theory and Practice of Uncertain Programming, Physica-Verlag, Heidelberg.
- Liu, Y.K, and Liu, B. (2003, a). A class of fuzzy random optimization: Expected value models, Information Sciences, Vol.155, Nos.1-2, 89-102.
- Liu, Y. K, and Liu, B. (2003, b). Fuzzy random variables: A scalar expected value opera-tor, Fuzzy Optimization and Decision Making, Vol.2, No.2, 143-160.
- Luenberger, D.G. (1997). Investment Science, Oxford University Press, Oxford.
- Maringer, D. (2005). Portfolio Management with Heuristic Optimization. Advances in Computational Management Science. Springer.
- Markowitz, H. (1952). Portfolio selection, Journal of Finance 7, 77–91.
- Mossin, J. (1966). Equilibrium in capital asset markets, Econometrica 34 (4), 768–783.
- Nather, W. (1997). Linear statistical inference for random fuzzy data. Statistics, 29, 221−240.
- Puri ML, and Ralescu D, Fuzzy random variables, Journal of Mathematical Analysis and Applications, Vol.114, 409-422, 1986.
- Sharpe, W.F. (1964). Capital asset prices: a theory of market equivalent under conditions of risk, Journal of Finance 19 (3), 425–442.
- Sheen, J.N. (2005). Fuzzy financial profitability analyses of demand side management alternatives from participant perspective, Information Sciences 169, 329–364.
- Smimou, K., Bector, C. R., & Jacoby, G. (2008). Portfolio selection subject to experts’ judgments International Review of Financial Analysis, 17, 1036–1054.
-
- Tanaka, H., Guo, P. (1999). Portfolio selection based on upper and lower exponential possibility distributions, European Journal of Operational Research 114, 115–126.
- Tanaka, H., Guo, P., Turksen, I.B. (2000). Portfolio selection based on fuzzy probabilities and possibility distributions, Fuzzy Sets and Systems 111, 387–397.
- Vercher, E., Bermúdez, J.D., Segura, J.V. (2007). Fuzzy portfolio optimization under downside risk measures, Fuzzy Sets and Systems 158, 769–782.
- Wang, X., Xu, W.J., Zhang, W.G., Hu, M.L. (2005). Weighted possibilistic variance of fuzzy number and its application in portfolio theory, Lecture Notes in Artificial Intelligance 3613 (2005) 148–155.
- Watada, J. (1997). Fuzzy portfolio selection and its applications to decision making, Tatra Mountains Mathematical Publications 13, 219–248.
- Yazenin, A.V. (2007). Possibilistic-probabilistic models and methods of portfolio optimization, in: Studies in Computational Intelligence, Vol. 36, Springer, Berlin, Heidelberg, Germany, pp. 241–259.
- Zadeh, L.A. (1978). Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1, 3–28.
- Zhang, W.G., Wang, Y.L. (2005). Portfolio selection: possibilistic mean–variance model and possibilistic efficient frontier, Lecture Notes in Computer Science 3521, 203–213.
- Zhang, W. G., Wang, Y. L., Chen, Z. P., Nie, Z. K. (2007). Possibilistic mean–variance models and efficient frontiers for portfolio selection problem, Information Sciences 177, 2787–2801.
- Ziemba, W.T., Mulvey, J. M. (1998). Worldwide Asset and Liability Modeling, Cambridge University Press, Cambridge.
- Abdelaziz, F.B., Lang, P., Nadeau, R. (1999). Efficiency in multiple criteria under uncertainty, Theory and Decision 47, 191–211.
- Abdelaziz, F.B., Mejri, S. (2001). Application of goal programming in a multi-objective reservoir operation model in Tunisia, European Journal of Operational Research 133, 352–361.
- Ammar, E. E. (2007). On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem, Information Sciences, Available Online 4 April.
- Aouni, B., Ben Abdelaziz, F., Martel, J. M. (2005). Decision-maker’s preferences modeling in the stochastic goal programming, European Journal of Operational Research 162, 610–618.
- Bawa, V.S., Lindenberg, E.B. (1977). Capital market equilibrium in a mean-lower partial moment framework, Journal of Financial Economics 5, 189–200.
- Campbell, J.Y., Lo, A.W., Mac Kinlay, A.C. (1997). The Econometrics of Finance Markets, Princeton University Press, Princeton, NJ.
- Carlsson, C., Fullér, R. (2001). On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122, 315–326.
- Chow. K., Denning. K. C., (1994). On variance and lower partial moment betas: the equivalence of systematic risk measures, Journal of Business Finance and Accounting 21, 231–241.
- Ehrgott, M., Klamroth, K., Schwehm, C. (2004). An MCDM approach to portfolio optimization, European Journal of Operational Research. 155, 752–770.
- Elton, E.J., Gruber, M.J. (1995). Modern Portfolio Theory and Investment Analysis, Wiley, New York.
- Glickman.T. S. (2008). Program portfolio selection for reducing prioritized securities, European Journal of Operational Research 190, 268–276.
- Gupta, P; Mehlawat, M. K; Saxena, A. (2008). Asset portfolio optimization using fuzzy mathematical programming. Information Sciences 178, 1734-1755.
- Hasuike, T., Katagiri, H., Ishii, H. (2009). Portfolio selection problems with random fuzzy variable returns. Fuzzy Sets and Systems. ARTICLE IN PRESS.
- Holland, J. Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, 1975.
- Huang, X. (2006). Fuzzy chance-constrained portfolio selection, Applied Mathematics and Computation 177, 500–507.
- Huang, X. (2007, a). Two new models for portfolio selection with stochastic returns taking fuzzy information, European Journal of Operational Research 180, 396–405.
- Huang, X. (2007, b). A new perspective for optimal portfolio selection with random fuzzy returns, Journal of Information Sciences 177, 5404–5414.
- Inuiguchi, M., Ramik, J. (2000). Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem, Fuzzy Sets and Systems 111, 3–28.
- Jorion, P. (1992). Portfolio optimization in practice, Financial Analysis Journal January–February 68–74.
- Katagiri, H., Ishii, H., Sakawa, M. (2004). On fuzzy random linear knapsack problems, Central European Journal of Operations Research 12, 59–70.
- Korner, R. (1997). On the variance of fuzzy random variables. Fuzzy Sets and Systems, 92, 83−93.
- Kruse R, and Meyer KD, Statistics with Vague Data, D. Reidel Publishing Company, Dordrecht, 1987.
- Kumar, P.C., Philippatos, G. C., Ezzell, J.R. (1978). Goal programming and the selection o portfolios by dual-purpose funds, The Journal of Finance 33, 303–310.
- Kwakernaak, H. K. (1978). Fuzzy random variables-I, Information Sciences 15, 1–29
- Kwakernaak, H.K. (1979). Fuzzy random variables-II, Information Sciences 17, 153–178
- Lacagnina, V., Pecorella, A. (2006). A stochastic soft constraints fuzzy model for a portfolio selection problem, Fuzzy Sets and Systems 157, 1317 – 1327.
- Lai, Y.J., Hwang, Ch. L. (1992). Fuzzy mathematical programming. Methods and applications. Springer-Verlag. Berlin, pp 257-270.
- Lee, S.M., Chesser, D. L. (1980). Goal programming for portfolio selection, The Journal of Portfolio Management 22–26.
- Leon, R.T., Liern, V., Vercher, E. (2002). Validity of infeasible portfolio selection problems: fuzzy approach, European Journal of Operational Researches 139, 178–189.
- Lin, Ch., Hsieh, P. J, (2004). A fuzzy decision support system for strategic portfolio management, Decision Support Systems, 38, 383-398
- Lintner, B. J. (1965). Valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics 47, 13–37.
- Liu, B. (2001). Fuzzy random chance-constrained programming, IEEE Transactions on Fuzzy Systems, Vol. 9, No. 5, 713-720.
- Liu, B. (2002). Theory and Practice of Uncertain Programming, Physica-Verlag, Heidelberg.
- Liu, Y.K, and Liu, B. (2003, a). A class of fuzzy random optimization: Expected value models, Information Sciences, Vol.155, Nos.1-2, 89-102.
- Liu, Y. K, and Liu, B. (2003, b). Fuzzy random variables: A scalar expected value opera-tor, Fuzzy Optimization and Decision Making, Vol.2, No.2, 143-160.
- Luenberger, D.G. (1997). Investment Science, Oxford University Press, Oxford.
- Maringer, D. (2005). Portfolio Management with Heuristic Optimization. Advances in Computational Management Science. Springer.
- Markowitz, H. (1952). Portfolio selection, Journal of Finance 7, 77–91.
- Mossin, J. (1966). Equilibrium in capital asset markets, Econometrica 34 (4), 768–783.
- Nather, W. (1997). Linear statistical inference for random fuzzy data. Statistics, 29, 221−240.
- Puri ML, and Ralescu D, Fuzzy random variables, Journal of Mathematical Analysis and Applications, Vol.114, 409-422, 1986.
- Sharpe, W.F. (1964). Capital asset prices: a theory of market equivalent under conditions of risk, Journal of Finance 19 (3), 425–442.
- Sheen, J.N. (2005). Fuzzy financial profitability analyses of demand side management alternatives from participant perspective, Information Sciences 169, 329–364.
- Smimou, K., Bector, C. R., & Jacoby, G. (2008). Portfolio selection subject to experts’ judgments International Review of Financial Analysis, 17, 1036–1054.
-
- Tanaka, H., Guo, P. (1999). Portfolio selection based on upper and lower exponential possibility distributions, European Journal of Operational Research 114, 115–126.
- Tanaka, H., Guo, P., Turksen, I.B. (2000). Portfolio selection based on fuzzy probabilities and possibility distributions, Fuzzy Sets and Systems 111, 387–397.
- Vercher, E., Bermúdez, J.D., Segura, J.V. (2007). Fuzzy portfolio optimization under downside risk measures, Fuzzy Sets and Systems 158, 769–782.
- Wang, X., Xu, W.J., Zhang, W.G., Hu, M.L. (2005). Weighted possibilistic variance of fuzzy number and its application in portfolio theory, Lecture Notes in Artificial Intelligance 3613 (2005) 148–155.
- Watada, J. (1997). Fuzzy portfolio selection and its applications to decision making, Tatra Mountains Mathematical Publications 13, 219–248.
- Yazenin, A.V. (2007). Possibilistic-probabilistic models and methods of portfolio optimization, in: Studies in Computational Intelligence, Vol. 36, Springer, Berlin, Heidelberg, Germany, pp. 241–259.
- Zadeh, L.A. (1978). Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1, 3–28.
- Zhang, W.G., Wang, Y.L. (2005). Portfolio selection: possibilistic mean–variance model and possibilistic efficient frontier, Lecture Notes in Computer Science 3521, 203–213.
- Zhang, W. G., Wang, Y. L., Chen, Z. P., Nie, Z. K. (2007). Possibilistic mean–variance models and efficient frontiers for portfolio selection problem, Information Sciences 177, 2787–2801.
- Ziemba, W.T., Mulvey, J. M. (1998). Worldwide Asset and Liability Modeling, Cambridge University Press, Cambridge.