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Full-Text Articles in Set Theory
Advanced Portfolio Theory: Why Understanding The Math Matters, Tom Arnold
Advanced Portfolio Theory: Why Understanding The Math Matters, Tom Arnold
Finance Faculty Publications
The goal of this paper is to motivate the use of efficient set mathematics for portfolio analysis [as seen in Roll, 1977] in the classroom. Many treatments stop at the two asset portfolio case (avoiding the use of matrix algebra) and an alarming number of treatments rely on illustration and templates to provide a heuristic sense of the material without really teaching how efficient portfolios are generated. This is problematic considering that the benefits of understanding efficient set mathematics go beyond portfolio analysis and into such topics as regression analysis (as demonstrated here).
Proceedings Of The First International Conference On Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability And Statistics, Florentin Smarandache
Proceedings Of The First International Conference On Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability And Statistics, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines the infinitesimals. Informally, an infinitesimal is an infinitely small number. Formally, x is said to be infinitesimal if and only if for all positive integers n one has xxx < 1/n. Let &>0 be a such infinitesimal number. The hyper-real number set is an extension of the real number set, which includes classes of infinite numbers and classes of infinitesimal numbers. Let’s consider the non-standard finite numbers 1+ = 1+&, where “1” is its standard part and “&” its non-standard part, …