**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30178

##### Portfolio Management: A Fuzzy Set Based Approach to Monitoring Size to Maximize Return and Minimize Risk

**Authors:**
Margaret F. Shipley

**Abstract:**

**Keywords:**
Portfolio Management,
Financial Market Monitoring,
Fuzzy Controller,
Fuzzy Logic,

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1072361

**References:**

[1]. de Korvin, A., Strawser, J., and Siegel, P. (1995). "An Application of Cost Control System to Cost Variance Analysis". Managerial Finance 21 (3), pp. 17-35.

[2]. Ellsberg, Daniel. (1961) "Risk, Ambiguity and the Savage Axioms". Quarterly Journal of Economics. 75(4), pp. 643- 669.

[3]. Slovic, P. and Tversky, A. (1974) "Who Accepts Savage-s Axioms". Behavioral Science. 19, pp. 368-373.

[4]. Kahneman, Daniel and Tversky, Amos. (1979) "Prospect Theory: An Analysis of Decisions under Risk". Econometrica. 47 (2), pp. 263-291.

[5]. Einhorn, Hillel J. and Hogarth, Robin M. (1985) "Ambuiguity and Uncertainty in Probabilistic Inference". Psychological Review. 92. pp. 433-461.

[6]. Einhorn, Hillel J. and Hogarth, Robin M. (1986) "Decision Making under Ambiguity". Journal of Business. 59(4), pp. S225-S250.

[7]. Markowitz, H. M. (1952) "Portfolio Selection." Journal of Finance. 7 (1). pp. 77-91.

[8]. Markowitz, H. M. (1959). Portfolio Selection, Efficient Diversification of Investments. New York: John Wiley and Sons, Inc.

[9]. Maller, R.A. and Turkington, D.A. (2003). "New Light on the Portfolio Problem". Mathematical Methods of Operations Research. 56(3), pp. 501-512.

[10]. Lim, Andrew and Zhou, Xun. (2002). "Mean-Variance Portfolio Selection with Random Parameters in a Complete Market". Mathematics of Operations Research. 27(1), pp. 101-120.

[11]. Kalyman, Basil. (1971) " Estimation Risk in Portfolio Selection Model". Journal of Financial & Quantitative Analysis. 6(1), pp. 559-582.

[12]. Gaivoronski, Alexei and De Lange, Petter. (2000). "An Asset Liability Management Model for Casualty Insurers: Complexity Reduction vs. Parameterized Decision Rules". Annals of Operations Research. 99(1-4), pp. 227-250.

[13]. Goldfarb, D. and Iyengar, G. (2003). "Robust Portfolio Selection Problems". Mathematics of Operations Research. 28(1), pp. 1-39.

[14]. Pachamanova, Dessislava (2006). " Handling Parameter Uncertainty in Portfolio Risk Minimization". Journal of Portfolio Management 32(4), pp. 70-78.

[15].Faboozi, Frank, Kolm, Petter, Pachamanova, Dessislave, Focardi, Sergio. (2007). "Robust Portfolio Optimization". Journal of Portfolio Management, 33(3), pp. 40-48.

[16]. El Ghaoui, Laurent, Oks, Maksim, and Oustry, Francois. (2003) "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach". Operations Research. 51(4) pp. 543-556.

[17]. Luciano, Elisa and Marena, Marina (2002) "Portfolio Value at Risk Bounds". International Transactions in Operational Research. 9, pp. 629-641.

[18]. Kozhan, Roman and Schmid, Wolfgang. (2009). "Asset Allocation with Distorted Beliefs and Transaction Costs". European Journal of Operational Research. 194 (1), pp.236-249

[19]. Sharpe, W.F. (1963). "A Simplified Model for Portfolio Analysis." Management Science. Pp. 277-293.

[20]. Grundke, Peter. (2009) "Importance Sampling for Integrated Market and Credit Portfolio Models". European Journal of Operational Research, 194 (1), pp. 206-226.

[21]. Balb├ís, Alejandro, Balb├ís, Raquel and Mayoral, Silvia (2009). "Portfolio Choice and Optimal Hedging with General Risk Functions: A Simplex-like algorithm". European Journal of Operational Research. 192(2), pp. 603-620.

[22]. Teo, K.L. and Yang, X.Q. (2001). "Portfolio Selection Problem with Minimax Type Risk Function". Annals of Operations Research. 10(1-4), pp. 333-349.

[23]. Duval, Yann and Featherstone, Allen (2002). "Interactivity and Soft Computing in Portfolio Management: Should Farmers Own Food and Agribusiness Stocks?" American Journal of Agriculture Economics. 84 (1), pp. 120-133.

[24]. Khoshnevisan, Mohammad, Vimba, Edgars and Bhattacharya, Sukanto (2007) "A Posited Fuzzy- Evolutionary Computational Model to Minimize the Tracking Error of an Option-Replicating Portfolio". Journal of Derivations & Hedge Funds 13(3), pp. 214-219

[25]. Black, F. and Scholes, M. (1973). "The Pricing of Options and Corporate Liabilities". Journal of Political Economy 81(3), pp. 637-654.

[26]. Jain, R.(1977) "A Procedure for Multiple Aspects Decision Making Using Fuzzy Sets." International Journal of System Science, 8, pp. 1-7.

[27]. Dubois,D. and Prade, H. (1979) "Decision Making under Fuzziness". Advances in Fuzzy Set Theory and Applications.(M.Gupta, R.Ragade, R. Yager, eds.) North Holland: Amsterdam.

[28]. Zebda, A. (1984) "The Investigation of Cost Variances: A Fuzzy Set Theory Approach". Decision Sciences, 15, pp. 359-388.

[29]. Zadeh, L. (1972). "A Rationale for Fuzzy Control". ASME Journal of Dynamic Systems Measurement and Control 94 Series G, pp. 3-4.

[30]. Mamdani, E. and Assilian, S. (1981). "An Experimenting Linguistic Synthesis with A Fuzzy Logic Controller". Fuzzy Reasoning and Its Applications, E.Mamdani and B. Gaines, eds. (Academic Press), pp. 311-323.

[31]. Yasunobu, S. and Miyamoto, S. (1985). "Automatic Train Operation System by Predictive Fuzzy Control". Industrial Applications of Fuzzy Control, M. Sugeno, ed. (North Holland), pp. 1-18.

[32]. Khoo, L., Yeong, H., and Tang, L. (1995). "Application of Fuzzy Reasoning to A Surface Treatment Process". Journal of Manufacturing Systems 14 (1), pp. 11-19.

[33]. Larkin, L. (1985). "A Fuzzy Logic Controller for Aircraft Flight Control". Industrial Applications of Fuzzy Control, M. Sugeno, ed. (North Holland), pp. 87-104.

[34]. Yagishta, O. Itoh, O., and Sugeno, M. (1990. "Application of Fuzzy Reasoning to the Water Purification Process". Industrial Applications of Fuzzy Control, M. Sugeno, ed. (North Holland), pp. 19-40.

[35]. Sugeno, M. and Murakami, K. (1985). "An Experimental Study on Fuzzy Parking Control Using A Model Car". Industrial Applications of Fuzzy Control, M. Sugeno, ed. (North Holland), pp. 19-40.

[36]. Yager, R. (1981). "A New Methodology for Ordinal Multiobjective Decisions Based on Fuzzy Sets". Decision Sciences . 12, pp. 589-600.

[37]. Shipley, M.F., Omer, K., and de Korvin, A. (1997) "A Fuzzy Controller for Adjusting Sample Size to Meet Quality Goals".Productivity and Quality Management Frontiers. (C.G.Thor, J.A.Edosomwan, R. Poupart, D.J. Sumanth, eds.), Norcross,Georgia: Engineering and Management Press Institute of Industrial Engineers, VI, 501-513.