The consumer’s demand functions defined to study contingent consumption plans

Angelini, Pierpaolo; Maturo, Fabrizio

doi:10.1007/s11135-021-01170-2

Cited by 7 publications

(5 citation statements)

References 39 publications

(29 reference statements)

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“…We are found inside the budget set of the decision maker. We are found inside a subset of R × R. Note that we also deal with the weighted average of n 2 estimated quantities of consumption for good 1 and good 2 that are jointly considered (see also [17] with regard to what is demanded for goods). They derive from the Cartesian product given by {x 1 1 , .…”

Section: Nonrandom Goods Demanded Under Claimed Conditions Of Certaintymentioning

confidence: 99%

Aggregate Bound Choices about Random and Nonrandom Goods Studied via a Nonlinear Analysis

Maturo

Angelini

2023

Mathematics

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In this paper, bound choices are made after summarizing a finite number of alternatives. This means that each choice is always the barycenter of masses distributed over a finite set of alternatives. More than two marginal goods at a time are not handled. This is because a quadratic metric is used. In our models, two marginal goods give rise to a joint good, so aggregate bound choices are shown. The variability of choice for two marginal goods that are the components of a multiple good is studied. The weak axiom of revealed preference is checked and mean quadratic differences connected with multiple goods are proposed. In this paper, many differences from vast majority of current research about choices and preferences appear. First of all, conditions of certainty are viewed to be as an extreme simplification. In fact, in almost all circumstances, and at all times, we all find ourselves in a state of uncertainty. Secondly, the two notions, probability and utility, on which the correct criterion of decision-making depends, are treated inside linear spaces over R having a different dimension in accordance with the pure subjectivistic point of view.

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Section: Nonrandom Goods Demanded Under Claimed Conditions Of Certaintymentioning

confidence: 99%

Aggregate Bound Choices about Random and Nonrandom Goods Studied via a Nonlinear Analysis

Maturo

Angelini

2023

Mathematics

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“…to denote that P(X 1 ) and P(X 2 ) depend on objective and subjective elements (see [28]). Given (P(X 1 ), P(X 2 )), a given investor also chooses a summarized element of the Fréchet class such that P(X 1 ) and P(X 2 ) never vary.…”

Section: A Full Analogy Between Properties Connected With Expected Re...mentioning

confidence: 99%

Probability Spaces Identifying Ordinal and Cardinal Utilities in Problems of an Economic Nature: New Issues and Perspectives

Angelini

2023

Mathematics

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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.

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“…where a ∈ R is an arbitrary constant. We consider infinite changes of origin in this way (Angelini and Maturo 2021a).…”

Section: A Random Good: Logical and Probabilistic Aspectsmentioning

confidence: 99%

Tensors Associated with Mean Quadratic Differences Explaining the Riskiness of Portfolios of Financial Assets

Angelini

Maturo

2023

JRFM

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Bound choices such as portfolio choices are studied in an aggregate fashion using an extension of the notion of barycenter of masses. This paper answers the question of whether such an extension is a natural fashion of studying bound choices or not. Given n risky assets, the question of why it is appropriate to treat only two risky assets at a time inside the budget set of the decision-maker is handled in this paper. Two risky assets are two goods. They are two marginal goods. The question of why they always give rise to a joint good inside the budget set of the decision-maker is addressed by this research work. A single risky asset is viewed as a double one using four nonparametric joint distributions of probability. The variability of a joint distribution of probability always depends on the state of information and knowledge associated with a given decision-maker. For this reason, two variability tensors are defined to identify the riskiness of the same risky asset. A multilinear version of the Sharpe ratio is shown. It is based on tensors. After computing the expected return on an n-risky asset portfolio, its riskiness is obtained using mean quadratic differences developed through tensors.

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The consumer’s demand functions defined to study contingent consumption plans

Cited by 7 publications

References 39 publications

Aggregate Bound Choices about Random and Nonrandom Goods Studied via a Nonlinear Analysis

Aggregate Bound Choices about Random and Nonrandom Goods Studied via a Nonlinear Analysis

Probability Spaces Identifying Ordinal and Cardinal Utilities in Problems of an Economic Nature: New Issues and Perspectives

Tensors Associated with Mean Quadratic Differences Explaining the Riskiness of Portfolios of Financial Assets

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