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 di erent 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 di erent 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.
Highlights
We consider a univariate risky asset denoted by X = {x1, x2, . . . , xm}
We find out a canonical expression of a portfolio of two univariate risky assets when it is viewed as a stand-alone entity
We have shown a canonical expression of a univariate risky asset
Summary
Probability can subjectively be distributed on particular points in the space of a random quantity. We have to note a very important point: the criteria for the evaluation of probability can be different (de Finetti, 1982b) They lead to an evaluation which is always subjective. Events and points are not bound by an evaluation of probability which is always the same because it is a predetermined evaluation It follows that probability viewed as a mass can coherently be moved by an investor according to his subjective opinion (Anscombe & Aumann, 1963)
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