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Matrices, defined as a set of numerical values arranged in a set of rows and columns has many applications in applied math, engineering, finance and accounting[1]. This is due to the fact that matrices make it easy to analyzed a set of a given. Numerical analysis as a major area of matrix finds many applications in modern day computations. The algorithms developed in the modern world make use of matrices to solve mathematical problems in finance. Matrices provide an infinite computation method that makes it possible to carry out the numerous financial calculations in the modern world. The theories learnt in matrices can be applied in financial engineering[2].
Financial engineering is a broader financial discipline that incorporates theory of finance, engineering methods, mathematical tools, and programming practice. Also defined as the use of technical methods with specific reference to numerical finance and computing finance, in the practical financial practice. Financial engineering should not be confused with any other engineering field; rather the field makes use of applied math, computed science, economic theories and statistics[3]. It simply means the use of technical tools to solve financial problems. Examples of financial engineers include the bank computer programmer and statisticians in any field.
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In banks and financial institutions today, financial institutions use matrices to solve their corporate balance sheets. Apart from the balance sheets, matrices find numerous applications in financial engineering. Some of the fields in financial engineering that matrix theory is applied include:
- Derivative pricing
- Financial execution
- Corporate finance
- Regulation of finance
- Managing risks
- Transactions
- Structured products
Computational aspects of matrix theory
The theoretical information on the matrix properties and applications or correlations in other fields can be used in practical, effective and precise financial calculations. A major domain of the matrix theory that finds application in the financial world is numerical linear algebra. Most problems are solved by considering the derivatives of the financial arguments or algorithms developed[4]. A sequence of xn series or financial argumentative are introduced or fed into the system which then solves the problems.
Matrix theory finds application in financial engineering, the field mainly taking advantage of
Matrix applications
There are numerous uses of matrices, both in numerical and applied science. Most of the applications merely take advantage of the close representation of set of numbers or facts that are input. Derivatives of the main financial functions or arguments provide effective financial solutions. For example if sales of a given family are dependent upon a number of given elements the matric representation of the information would be like: y=a1n1+a2n2+a3n3+……..+axnx into the system[5]. The financial constants would be dictated by the variables. With knowledge of matrices, the derivatives can be found hence solving the problem at hand[6].
A good example to illustrate this is the economics field is where payoff matrices comprising two players; this depends on the finite pattern of options operators choose. Complex numbers or digits can easily be represented a simple matrix pattern. Logical matrices can be used to reduce workload in the financial calculations, since it output only two possibilities. Executable calculations are output as 1 and those that cannot be executed as 0.
Points of minima and maxima can be calculated. The points of minima or maxima could be could be good financial indicators to the companies, in terms of how to maximize their profits. What are the dependent variables? What are the independent variables? How does, say, the variation of an input of a commodity or an entity, affect the other components of the financial setting. The qualitative analysis of the results, financial graphs, and set of financial matrices could go a long way to offer invaluable information to help financial engineers manage or reduce risks[7]. Corporate finance, in terms of regulation and execution benefits a lot from matrix theory.