Maximum Varma Entropy Distribution with Conditional Value at Risk Constraints

Liu, Chang; Chang, Chuo; Chang, Zhe

doi:10.3390/e22060663

Cited by 7 publications

(4 citation statements)

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“…The weight coefficient analysis consists of three main steps: constructing the priority relation judgment matrix, constructing the fuzzy consistent judgment matrix, and calculating the weight coefficient ( 26 ). This paper adopts AHP based on three scales to determine the weight of each index.…”

Section: Proposed Methodsmentioning

confidence: 99%

Analysis of the Safety Factors of Municipal Road Undercrossing Existing Bridge Based on Fuzzy Analytic Hierarchy Process Methods

Yang

Chen

Tang

2021

Transportation Research Record: Journal of the Transportation R

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Increasing traffic volume and insufficient road lanes often require municipal roads to be reconstructed and expanded. Where a road passes under a bridge, the reconstruction and expansion project will inevitably have an impact on the bridge. To evaluate the safety impact of road engineering projects on bridges, this paper evaluates the safety of the roads and ancillary facilities of highway bridges involved in municipal road engineering projects. Based on a comprehensive analysis of the safety factors of municipal roads undercrossing existing bridges, a fuzzy comprehensive analytic hierarchy process (AHP) evaluation method for the influence of road construction on the safety of existing bridges is proposed. First, AHP is used to select 11 evaluation factors. Second, the target layer, criterion layer, and index layer of evaluation factors are established, then a safety evaluation factor system is formed. The three-scale AHP model is used to determine the weight of assessment indexes. Third, through the fuzzy comprehensive AHP evaluation model, the fuzzy hierarchical comprehensive evaluation is carried out for the safety assessment index system. Finally, the fuzzy comprehensive evaluation method is applied to the engineering example of a municipal road undercrossing an existing expressway bridge. The comprehensive safety evaluation of the existing bridge reflects the practicability and feasibility of the method. It is expected that, with further development, the method will improve the decision-making process in bridge safety assessment systems.

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Section: Proposed Methodsmentioning

confidence: 99%

Analysis of the Safety Factors of Municipal Road Undercrossing Existing Bridge Based on Fuzzy Analytic Hierarchy Process Methods

Yang

Chen

Tang

2021

Transportation Research Record: Journal of the Transportation R

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“…For other details and applications of the Varma entropy, we recommend [33][34][35][36][37][38]. We emphasize the fact that the Varma entropy is a generalization of the Rényi entropy, which is a well-known entropy for its applications (see [8,[39][40][41][42][43][44][45][46]).…”

Section: Preliminariesmentioning

confidence: 99%

Discrete Entropies of Chebyshev Polynomials

Sfetcu,

Preda

2024

Mathematics

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Because of its flexibility and multiple meanings, the concept of information entropy in its continuous or discrete form has proven to be very relevant in numerous scientific branches. For example, it is used as a measure of disorder in thermodynamics, as a measure of uncertainty in statistical mechanics as well as in classical and quantum information science, as a measure of diversity in ecological structures and as a criterion for the classification of races and species in population dynamics. Orthogonal polynomials are a useful tool in solving and interpreting differential equations. Lately, this subject has been intensively studied in many areas. For example, in statistics, by using orthogonal polynomials to fit the desired model to the data, we are able to eliminate collinearity and to seek the same information as simple polynomials. In this paper, we consider the Tsallis, Kaniadakis and Varma entropies of Chebyshev polynomials of the first kind and obtain asymptotic expansions. In the particular case of quadratic entropies, there are given concrete computations.

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“…Since the tail region of stock price distribution follows the power law [32,33], which is signifcantly diferent from the normal distribution, it does not make sense to discuss variance in these circumstances. In order to avoid the use of variance as a constraint when optimizing portfolio entropy, following [34,35], we apply the value-at-risk and expected shortfall constraints instead of the variance constraint. In this way, the probability density distribution of return is more theoretically reasonable.…”

Section: Introductionmentioning

confidence: 99%

Modelization and Calibration of the Power-Law Distribution in Stock Market by Maximization of Varma Entropy

Liu,

Chang

2023

Complexity

Self Cite

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Proper description of the return distribution is crucial for investment practitioners. The underestimation of the tail risk may lead to severe consequences, even for assets with moderate fluctuations. However, many empirical studies found that the distribution tails of many financial assets drop off more slowly than the Gaussian distributions. Therefore, we intend to model and calibrate the heavy tails observed in financial fluctuations in this study. By maximizing the Varma entropy with value-at-risk and expected shortfall constraints, we obtain the probability distribution of stock return and observe that the tail of stock return distribution is a power law. Since the variance of the real stock portfolio may be a random variable, using the mean-VaR-ES constraints to maximize the Varma entropy effectively avoids the problem of assuming that the variance is a constant value under the traditional mean-variance constraint. Therefore, the deduced theoretical model would be more consistent with the real market. Using high-frequency data from China’s stock markets, we calibrate our theoretical model and give the concrete form of probability density distribution p(x) for different time intervals. The calibration results show that the tail of the stock return distribution is a power law with most of the power-law orders between −2 and −7. We prove the robustness of our results by calibrating the Varma entropy for S&P 500 of the USA stock market and different stock market indices in China’s A-share market. Our research’s findings not only offer a theoretical perspective for researchers but also give investing professionals a theoretical foundation on which to base their decisions.

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Maximum Varma Entropy Distribution with Conditional Value at Risk Constraints

Cited by 7 publications

References 50 publications

Analysis of the Safety Factors of Municipal Road Undercrossing Existing Bridge Based on Fuzzy Analytic Hierarchy Process Methods

Analysis of the Safety Factors of Municipal Road Undercrossing Existing Bridge Based on Fuzzy Analytic Hierarchy Process Methods

Discrete Entropies of Chebyshev Polynomials

Modelization and Calibration of the Power-Law Distribution in Stock Market by Maximization of Varma Entropy

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