Abstract
This paper describes methodology of dealing with financial modeling under uncertainty with risk and vagueness aspects. An approach to modeling risk by the Conditional Value at Risk methodology under imprecise and soft Conditions is solved. It is supposed that the input data and problem conditions are difficult to determine as real number or as some precise distribution function. Thus, vagueness is modeled through the fuzzy numbers of linear T-number type. The combination of risk and vagueness is solved by fuzzy-stochastic methodology. Illustrative example is introduced.
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References
Alexander, S., Coleman, T.F., Li, Y.: Minimizing CVaR and VaR for a portfolio of derivatives. Journal of Banking and Finance 30, 583–605 (2006)
Ammar, E.E.: On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem. Information Sciences 178, 468–484 (2008)
Artzner, P., Eber, F., Eber, J.M., Heath, D.: Coherent measures of risk. Mathematical Finance 9, 203–228 (1999)
Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Management Science 17, 141–164 (1970)
Delbaen, F.: Coherent measures of risk on general probability spaces. In: Sandmann, K., Schonbucher, P.J. (eds.) Advances in Finance and Stochastics, Essays in Honor of Dieter Sondermann, pp. 1–37. Springer, Berlin (2002)
Duffie, D., Pan, J.: An overview of value at risk. Journal of Derivatives, 7–49 (Spring 1997)
Jorion, P.: Value at Risk. Mc-Graw Hill
Olsen, R.A., Throuhton, G.H.: Are risk premium anomalies caused by ambiguity? Financial Analyst Journal (March/April 2000)
Ostermark, R.: Fuzzy linear constrains in the capital asset pricing model. Fuzzy Sets and Systems 30, 93–102 (1989)
Pisoult, E.: Quantifying the risk of trading. In: Dempster, M.A.H. (ed.) Risk Management: Value at Risk and Beyond. Cambridge University Press
Rockafellar, R.T., Uryasev, S.P.: Optimization of conditional value-at-risk. J. Risk 2, 21–41 (2000)
Simonelli, M.R.: Fuzziness in valuing financial instruments by certainty equivalents. European Journal of Operational Research 135, 296–302 (2001)
Tanaka, H., Guo, P., Turksen, I.B.: Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets and Systems 111, 387–397 (2000)
Tseng, F.M., Yu, G.H., et al.: Fuzzy ARIMA model for forecasting the foreign exchange market. Fuzzy Sets and Systems 118, 9–19 (2001)
Young, V.R., Zariphopoulu, T.: Computation of distorted probabilities for diffusion processes via stochastic control methods. Insurance, Mathematics and Economics 27, 1–18 (2000)
Zmeskal, Z.: Application of the fuzzy-stochastic methodology to appraising the firm value as a European call option. European Journal of Operational Research 135(2), 303–310 (2001)
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Tang, Sf., He, Yy. (2013). Conditional Value at Risk Methodology under Fuzzy-Stochastic Approach. In: Huang, DS., Bevilacqua, V., Figueroa, J.C., Premaratne, P. (eds) Intelligent Computing Theories. ICIC 2013. Lecture Notes in Computer Science, vol 7995. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39479-9_20
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DOI: https://doi.org/10.1007/978-3-642-39479-9_20
Publisher Name: Springer, Berlin, Heidelberg
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