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Fuzzy Applications In Finance and Investment

In the Name of God. School of Economic Sciences. Fuzzy Applications In Finance and Investment. Dr. K.Pakizeh k.Dehghan Manshadi E.Jafarzade. 1390 March. 1. Forecasting Demand Using Fuzzy Averaging. Forecasting Demand Using Fuzzy Averaging.

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Fuzzy Applications In Finance and Investment

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  1. In the Name of God School of Economic Sciences Fuzzy Applications In Finance and Investment Dr. K.Pakizeh k.Dehghan Manshadi E.Jafarzade 1390 March

  2. 1 Forecasting Demand Using Fuzzy Averaging

  3. Forecasting Demand Using Fuzzy Averaging Five experts are asked to forecast the annual demand for a new product using Fuzzy Delphi technique which requires use of triangular numbers Ai = (a(i) 1 ; a(i) M; a(i) 2 ); i = 1; …..; 5. Here a(i) 1 is the smallest number of units to be produced, a(i) M is the most likely number of units, and a(i) 2 is the largest number of units. The experts opinions are shown on Table bellow: Forecasting Demand Using Fuzzy Averaging Experts estimates for annual demand for a new product.

  4. Forecasting Demand Using Fuzzy Averaging The Defuzzied Average

  5. 2 Fuzzy Zero-Based Budgeting

  6. Fuzzy Zero-Based Budgeting The fuzzy zero-based budgeting method uses triangular numbers to model fuzziness in budgeting. it is more realistic to use fuzzy data instead of crisp data. Consider a company with several decision centers, say A;B; and C. Assume that the decision makers agree on some preliminary budgets using a specified number of budget levels for each center depending on its importance. The budgets are expressed in terms of triangular fuzzy numbers obtained by certain procedure . Fuzzy Zero-Based Budgeting The following possible budget levels were suggested: improved for the centerA;A0 < A1 < A2; for the centerB;B0 < B1; for the centerC;C0 < C1 < C2: normal minimal

  7. The total budget available to the company is limited but it is flexible and could be expressed by a right trapezoidal number Lof the type shown in Fig. bellow with membership function: Fuzzy Zero-Based Budgeting Total available budget.

  8. The decision makers follow a step by step budget allocation procedure according to the importance of each center in their opinion. Fuzzy Zero-Based Budgeting where

  9. Example The limited available budget L given by and Fuzzy Zero-Based Budgeting

  10. Fuzzy Zero-Based Budgeting Cumulative budgets. NOTE: The budget of center B is at level 0 (smaller than normal ); the decision makers may consider the option to close this center and redistribute the money to the other two centers which are more important.

  11. 3 Fuzzy Valuation

  12. Fuzzy Valuation Valuation is One of the most important aspect of Investment and Finance Problems. Although there are many methods in valuation, but most of them are based on calculation of present value of cash flows. In most cases its assumed that the discount rate is fixed and deterministic. But we know that such assumption can rarely be true. So one of the applicable method in order to consider a probabilistic discount rate is Fuzzy procedure. Here this procedure is introduced with an example. Fuzzy Valuation Fi = cash flow in period I R= discount rate PV=ordinary present value (its with uncertainty)

  13. Now we assume a fuzzy discount rate and rewrite the PV formula as bellow: Fuzzy Valuation Discount rate in period i (triangular fuzzy number) Example

  14. Fuzzy Valuation

  15. 4 Portfolio Selection Based on the Fuzzy Decision Theory

  16. Portfolio Selection Based on the Fuzzy Decision Theory with the membership function: Portfolio Selection Based on the Fuzzy Decision Theory Furthermore, the optimal decision is defined by the following non-fuzzy subset

  17. An investor can construct a portfolio based on m potential market scenarios from an investment universe of n assets with and xmax i being the minimum and the maximum weight of the ith asset, respectively. Let Rik denote the return of the ith asset for the kth market scenario and let Rk(x) = n i=1 Rikxi denote the portfolio return for the kth scenario, at the end of the investment period. For each scenario, the investor may have a target range for the expected return, over the investment period. Denoting Rmin k and Rmax k as the minimum and the maximum expected returns, respectively, for the kth market scenario, and characterizing the degree of the investor’s satisfaction with portfolio x for the kth scenario as the following linear membership function: Portfolio Selection Based on the Fuzzy Decision Theory

  18. portfolio selection model can be written as follow: Portfolio Selection Based on the Fuzzy Decision Theory

  19. References: [1] Yong Fang and et.al;Fuzzy portfolio optimization;theory and methods; [2] George Bojadziev and Maria Bojadziev;Fuzzy Logic for Business,Finance, and Management; [3] Ludmila Dymowa;Soft computing in Economics and Finance; [4]Kaufman, Arnold &Madan M.Gupta,1991,Fuzzy mathematical models in engineering and management science,Elsevier Science Publications. References

  20. Thanks for Your Attention..…

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