Abstract
An approach to deal with fuzziness in financial markets by using random matrix theory is proposed. Recent results provide evidence of their importance in understanding the structure of variance-covariance matrix. Formulations that might go beyond the mean-variance model in financial optimization are suggested.
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References
P. Pardalos (1997) Optimization Techniques for Portfolio Selection, in New Operational Approaches for Financial Modelling, C. Zopounidis (ed), PhysicaVerlag, pp. 19–33.
H. Markowitz (1952) “Portfolio Selection”, The Journal of Finance, vol. 7, No. 1, pp. 77–91.
C. Porter and N. Rosenzweig (1960) “Statistical Properties of Atomic and Nuclear Spectra”, Annales Academiae Scientiarum Fennicae, Serie A, VI Physica, 44, pp. 1–66.
F. Dyson and M. Mehta (1963) Journal of Math. Phys, vol. 4, pp. 701–712.
M. Mehta (1995) Random Matrices Academic Press, New York.
E. Wigner (1951) Ann. Math, vol 53, p. 36.
V. Plerou, P. Gopikrishnan, B. Rosenow, L. Amaral and E. Stanley (1999) “Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series”, Physical Review Letters, vol. 83, No. 7, pp. 1471–1475.
A. Sengupta and P. Mitra cond-mat/9709283.
T. Brody et al (1981) Rev. Mod. Phys., vol. 53, p. 385.
L. Laloux, P. Cizeau, J-P. Bouchaud and M. Porters (1999) “Noise Dressing of Financial Correlation Matrices”, Physical Review Letters, vol. 83, No. 7, pp. 1467–1470.
E. Elton and M. Gruber (1995) Modern Portfolio Theory and Investment Analysis, J. Wiley and Sons, New York.
A. Edelman (1988) SIAM J. Matrix Anal. Appl, vol. 9, p. 543.
M. Bowick and E. Brezin (1991) Phys. Lett. B, vol. 268, p. 21.
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Korotkikh, G. (2002). On Understanding the Structure of Variance-Covariance Matrix for Dealing with Fuzziness in Financial Markets. In: Dimitrov, V., Korotkich, V. (eds) Fuzzy Logic. Studies in Fuzziness and Soft Computing, vol 81. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1806-2_15
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DOI: https://doi.org/10.1007/978-3-7908-1806-2_15
Publisher Name: Physica, Heidelberg
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