We show a canonical expression of a univariate risky asset. We find out a canonical expression of the product of two univariate risky assets when they are jointly considered. We find out a canonical expression of a portfolio of two univariate risky assets when it is viewed as a stand-alone entity. We prove that a univariate risky asset is an isometry. We define different distributions of probability on R inside of metric spaces having different dimensions. We use the geometric property of collinearity in order to obtain this thing. We obtain the expected return on a portfolio of two univariate risky assets when it is viewed as a stand-alone entity. We also obtain its variance. We show that it is possible to use two different quadratic metrics in order to analyze a portfolio of two univariate risky assets. We consider two intrinsic properties of it. If a portfolio of two univariate risky assets is viewed as a stand-alone entity then it is an antisymmetric tensor of order 2. What we say can be extended to a portfolio of more than two univariate risky assets.

A portfolio of risky assets and its intrinsic properties / Angelini, Pierpaolo. - In: JOURNAL OF MATHEMATICS RESEARCH. - ISSN 1916-9795. - (2020).

A portfolio of risky assets and its intrinsic properties

pierpaolo angelini
2020

Abstract

We show a canonical expression of a univariate risky asset. We find out a canonical expression of the product of two univariate risky assets when they are jointly considered. We find out a canonical expression of a portfolio of two univariate risky assets when it is viewed as a stand-alone entity. We prove that a univariate risky asset is an isometry. We define different distributions of probability on R inside of metric spaces having different dimensions. We use the geometric property of collinearity in order to obtain this thing. We obtain the expected return on a portfolio of two univariate risky assets when it is viewed as a stand-alone entity. We also obtain its variance. We show that it is possible to use two different quadratic metrics in order to analyze a portfolio of two univariate risky assets. We consider two intrinsic properties of it. If a portfolio of two univariate risky assets is viewed as a stand-alone entity then it is an antisymmetric tensor of order 2. What we say can be extended to a portfolio of more than two univariate risky assets.
2020
collinearity; affine tensor; antisymmetric tensor; isometry; α-norm; α-product
01 Pubblicazione su rivista::01a Articolo in rivista
A portfolio of risky assets and its intrinsic properties / Angelini, Pierpaolo. - In: JOURNAL OF MATHEMATICS RESEARCH. - ISSN 1916-9795. - (2020).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1429481
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