Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

MODIFIED MULTIPLICATIVE UPDATE ALGORITHMS FOR COMPUTING THE NEAREST CORRELATION MATRIX

  • Yin, Jun-Feng (Department of Mathematics, Tongji University) ;
  • Huang, Yumei (School of Mathematics and Statistics, Lanzhou University)
  • Received : 2011.04.18
  • Accepted : 2011.07.16
  • Published : 2012.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

A modified multiplicative update algorithms is presented for computing the nearest correlation matrix. The convergence property is analyzed in details and a sufficient condition is given to guarantee that the proposed approach will not breakdown. A number of numerical experiments show that the modified multiplicative updating algorithm is efficient, and comparable with the existing algorithms.

Keywords

References

  1. A. A. Al-Subaihi, Simulating Correlated Multivariate Pseudorandom Numbers, J. Stat. Soft., vol. 9(2004), 1-20.
  2. Z.-Z. Bai, G. H. Golub, L.-Z. Lu, J.-F. Yin, Block triangular and skew-Hermitian splitting methods for positive-definite linear systems, SIAM Journal on Scientific Computing, 26(2005), 844-863. https://doi.org/10.1137/S1064827503428114
  3. Z.-Z. Bai, G. H. Golub, M. K. Ng, Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, SIAM Journal on Matrix Analysis and Applications, 24(2003), 603-626. https://doi.org/10.1137/S0895479801395458
  4. N. Higham, Computing a nearest symmetric positive semidefinite matrix, Linear Algebra and its Applications, 103(1988), 103-118. https://doi.org/10.1016/0024-3795(88)90223-6
  5. N. Higham, Computing the nearest correlation matrix-a problem from finance. IMA Journal of Numerical Analysis, 22(2002), 329-343. https://doi.org/10.1093/imanum/22.3.329
  6. P. Jackel and R. Rebonato, The most general methodology for creating a valid correlation matrix for risk management and option pricing purposes, Journal of Risk, 2(1999), 17-28.
  7. P. H. Kupiec, Stress testing in a value at risk framework. Journal of Derivatives, 6(1998), 7-24.
  8. D. D. Lee and H. S. Seung, Algorithms for non-negative matrix factorization. In T. K. Leen, T. G. Dietterich, and V. Tresp, editors, Advances in Neural Information Processing Systems, 13(2001), 556-562.
  9. K. Schottle and R. Werner, Improving \the most general methodology to create a valid correlation matrix", Risk Analysis IV, Management Information Systems, 9(2004), 701-712.
  10. P. Sonneveld, J.J.I.M. van Kan, X. Huang and C. W. Oosterlee, Nonnegative matrix factorization of a correlation matrix, Linear Algebra and its Applications, 431(2009), 334-349. https://doi.org/10.1016/j.laa.2009.01.004
  11. D.-X. Xie, Y.-P. Sheng and Z.-Z. Zhang, Computing the nearest bisymmetric positive semidefinite matrix under the spectral restriction, Numerical Mathematics: A Journal of Chinese Universities English Series, 12(2003), 71-82.