Mathematics, Vol. 11, Pages 4280: Probability Spaces Identifying Ordinal and Cardinal Utilities in Problems of an Economic Nature: New Issues and Perspectives

Mathematics, Vol. 11, Pages 4280: Probability Spaces Identifying Ordinal and Cardinal Utilities in Problems of an Economic Nature: New Issues and Perspectives

Mathematics doi: 10.3390/math11204280

Authors: Pierpaolo Angelini

Prevision bundles identifying expected returns on risky assets are established. A probability space associated with risky assets is defined. In this research work, the optimization principle is based on the notion of distance. This is because problems of an economic nature are not handled in an axiomatic or intrinsic way, but they are investigated with regard to a given coordinate system. The latter is shown to be invariant. The notion of mathematical expectation applied to summarizing both monetary values and utilities is treated. Such a notion is extended to study portfolios of financial assets. Objective conditions of coherence connected with the notion of mathematical expectation are extended. Rational behaviors towards risk are based on them. A model representing diagrams considered inside the same coordinate system is shown. Such a model identifies as many optimal choices as pair comparisons it is possible to take into account in order to obtain a multilinear measure. The latter is the expected return on a specific portfolio of financial assets.