The non-integer higher-order Stochastic dominance

Bi, Hongwei; Zhu, Wei

doi:10.1016/j.orl.2018.12.006

Cited by 6 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One of Fishburn's important result is the development of the continuum of SD rules that extends the orders of SD from positive integers to real numbers no less than 1 [15,16]. Fractional-order SD is currently still an active research topic, e.g., [17][18][19], as integral-order SD is simply too coarse in some applications. For example, first-order SD models the nonsatiable individuals with increasing utilities, and second-order SD models the non-satiable and risk-averse individuals with increasing concave utilities, but the cases between the substantial gap of the two orders are not captured.…”

Section: Of 15mentioning

confidence: 99%

Discrete Analogue of Fishburn’s Fractional-Order Stochastic Dominance

Yin¹,

Wang²,

Mak³

et al. 2023

Preprint

View full text Add to dashboard Cite

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In early days, Fishburn investigated SD from the view of distributions and we refer this perspective as Fishburn’s SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD may not be generalized directly since some properties of fractional calculus do not have a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD from the view of distributions. We generalize the order of SD by Lizama’s fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be generalized directly from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle them.

show abstract

Section: Of 15mentioning

confidence: 99%

Discrete Analogue of Fishburn’s Fractional-Order Stochastic Dominance

Yin¹,

Wang²,

Mak³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Because U γ is empty except it contains zero function in this case. But we can define the high-order fractional reference dependent stochastic dominance, denoted by (n + γ)-SD r , by using the consumption utility function class introduced in [4]. In this paper, we focus on the development of (1 + γ)-SD r .…”

Section: The Definitionsmentioning

confidence: 99%

Fraction-Degree Reference Dependent Stochastic Dominance

Yang

Zhao

Chen

et al. 2022

Methodol Comput Appl Probab

View full text Add to dashboard Cite

For addressing the Allis-type anomalies, a fractional degree reference dependent stochastic dominance rule is developed which is a generalization of the integer degree reference dependent stochastic dominance rules. This new rule can effectively explain why the risk comparison does not satisfy translational invariance and scaling invariance in some cases. The rule also has a good property that it is compatible with the endowment effect of risk. This rule can help risk-averse but not absolute risk-averse decision makers to compare risks relative to reference points. We present some tractable equivalent integral conditions for the fractional degree reference dependent stochastic dominance rule, as well as some practical applications for the rule in economics and finance.

show abstract

“…One of Fishburn's important results is the development of the continuum of SD rules that extends the orders of SD from positive integers to real numbers no less than one [15,16]. Fractional-order SD is currently still an active research topic, e.g., [17][18][19], as integral-order SD is simply too coarse in some applications. For example, first-order SD models the insatiable individuals with increasing utilities, and second-order SD models the insatiable and risk-averse individuals with increasing concave utilities, but the cases between the substantial gap of the two orders cannot be well captured.…”

Section: Introductionmentioning

confidence: 99%

Discrete Analogue of Fishburn’s Fractional-Order Stochastic Dominance

Yin

Wang²,

Mak

et al. 2023

Axioms

View full text Add to dashboard Cite

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In the early days, Fishburn investigated SD from the view of distributions, and we refer this perspective as Fishburn’s SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD cannot be directly generalized, because some properties of fractional calculus may not possess a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD for discrete utilities from the view of distributions. We generalize the order of SD by Lizama’s fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be directly generalized from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle it for further applications in mathematics and computer science.

show abstract

The non-integer higher-order Stochastic dominance

Cited by 6 publications

References 11 publications

Discrete Analogue of Fishburn’s Fractional-Order Stochastic Dominance

Discrete Analogue of Fishburn’s Fractional-Order Stochastic Dominance

Fraction-Degree Reference Dependent Stochastic Dominance

Discrete Analogue of Fishburn’s Fractional-Order Stochastic Dominance

Contact Info

Product

Resources

About