Matrix Function with Application in Financial Mathematics
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Published:
Nov 27, 2018
Keywords:
Function of Matrix Diagonalizable Matrix Jordan Canonical Form Power Function of Matrix Transcendental Function of Matrix
Main Article Content
Abstract
This article presents a concept to define a function of matrix. Start by defining a power function of matrix is then expanded to the concept of the
definition of any function of matrix. Some calculating-examples are provided to clearly understand. An application to financial mathematics is shown.
Article Details
How to Cite
Witayakiattilerd, W. (2018). Matrix Function with Application in Financial Mathematics. Mathematical Journal by The Mathematical Association of Thailand Under The Patronage of His Majesty The King, 62(692), 1–18. Retrieved from https://ph02.tci-thaijo.org/index.php/MJMATh/article/view/157365
Section
Academic Article
References
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[2] F. R. Gantmacher, The Theory of matrices, New York: Chelsea publishing company, 1959.
[3] Hong Sung Pyo, Chapter 8: Jordan Canonical Forms, from http://math.postech.ac.kr/~sungpyo/LinearAlge-2007/Chap8.pdf
[4] J. W. Polderman and J. C. Willems, Introduction to Mathematical Systems Theory: A Behavioral Approach, New York: Springer Verlag, 1998.
[5] Jean-Philippe Bouchaud and Marc Potters, Financial Applications of Random Matrix Theory: a short review, from
http://math.postech.ac.kr/~sungpyo/LinearAlge-2007/Chap8.pdf., 2009.
[6] John H. Cochrane, Time Series for Macroeconomics and Finance, Chicago: University of Chicago, 1997.
[7] Lawrence C. Evans, An Introduction to Mathematical Optimal Control Theory, Berkeley: University of California, 1983.
[8] Nicholas J. Higham, Function of Matrices: Theory and Computation, Philadelphia: Society for Industrial and Applied Mathematics, 2008.
[9] Wolfgang Ertel, Advanced Mathematics for Engineers, Hochschule Ravensburg-Weingarten University of Applied Sciences, 2008.