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2352 KiB

Open AccessArticle

Properties of Risk Measures of Generalized Entropy in Portfolio Selection

by Rongxi Zhou, Xiao Liu, Mei Yu and Kyle Huang

Entropy 2017, 19(12), 657; https://doi.org/10.3390/e19120657 - 01 Dec 2017

Cited by 16 | Viewed by 4134

This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both [...] Read more.

This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both fuzziness and randomness. We discover that none of the risk measures satisfy all six of the following properties, which various scholars have associated with effective risk measures: Monotonicity, Translation Invariance, Sub-additivity, Positive Homogeneity, Consistency and Convexity. Measures based on Fuzzy Entropy, Credibility Entropy, and Sine Entropy all exhibit the same properties: Sub-additivity, Positive Homogeneity, Consistency, and Convexity. These measures based on Information Entropy and Hybrid Entropy, meanwhile, only exhibit Sub-additivity and Consistency. Cumulative Residual Entropy satisfies just Sub-additivity, Positive Homogeneity, and Convexity. After identifying these properties, we develop seven portfolio models based on different risk measures and made empirical comparisons using samples from both the Shenzhen Stock Exchange of China and the New York Stock Exchange of America. The comparisons show that the Mean Fuzzy Entropy Model performs the best among the seven models with respect to both daily returns and relative cumulative returns. Overall, these results could provide an important reference for both constructing effective risk measures and rationally selecting the appropriate risk measure under different portfolio selection conditions. Full article

(This article belongs to the Special Issue Entropic Applications in Economics and Finance)

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509 KiB

Open AccessArticle

Quantal Response Statistical Equilibrium in Economic Interactions: Theory and Estimation

by Ellis Scharfenaker and Duncan K. Foley

Entropy 2017, 19(9), 444; https://doi.org/10.3390/e19090444 - 25 Aug 2017

Cited by 24 | Viewed by 6913

Abstract

Social science addresses systems in which the individual actions of participants interacting in complex, non-additive ways through institutional structures determine social outcomes. In many cases, the institutions incorporate enough negative feedback to stabilize the resulting outcome as an equilibrium. We study a particular [...] Read more.

Social science addresses systems in which the individual actions of participants interacting in complex, non-additive ways through institutional structures determine social outcomes. In many cases, the institutions incorporate enough negative feedback to stabilize the resulting outcome as an equilibrium. We study a particular type of such equilibria, quantal response statistical equilibrium (QRSE) using the tools of constrained maximum entropy modeling developed by E. T. Jaynes. We use Adam Smith’s theory of profit rate maximization through competition of freely mobile capitals as an example. Even in many cases where key model variables are unobserved, it is possible to infer the parameters characterizing the equilibrium through Bayesian methods. We apply this method to the Smithian theory of competition using data where firms’ profit rates are observed but the entry and exit decisions that determine the distribution of profit rates is unobserved, and confirm Smith’s prediction of the emergence of an average rate of profit, along with a characterization of equilibrium statistical fluctuations of individual rates of profit. Full article

(This article belongs to the Special Issue Entropic Applications in Economics and Finance)

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1296 KiB

Open AccessArticle

Transfer Entropy for Nonparametric Granger Causality Detection: An Evaluation of Different Resampling Methods

by Cees Diks and Hao Fang

Entropy 2017, 19(7), 372; https://doi.org/10.3390/e19070372 - 21 Jul 2017

Cited by 10 | Viewed by 5986

Abstract

The information-theoretical concept transfer entropy is an ideal measure for detecting conditional independence, or Granger causality in a time series setting. The recent literature indeed witnesses an increased interest in applications of entropy-based tests in this direction. However, those tests are typically based [...] Read more.

The information-theoretical concept transfer entropy is an ideal measure for detecting conditional independence, or Granger causality in a time series setting. The recent literature indeed witnesses an increased interest in applications of entropy-based tests in this direction. However, those tests are typically based on nonparametric entropy estimates for which the development of formal asymptotic theory turns out to be challenging. In this paper, we provide numerical comparisons for simulation-based tests to gain some insights into the statistical behavior of nonparametric transfer entropy-based tests. In particular, surrogate algorithms and smoothed bootstrap procedures are described and compared. We conclude this paper with a financial application to the detection of spillover effects in the global equity market. Full article

(This article belongs to the Special Issue Entropic Applications in Economics and Finance)

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430 KiB

Open AccessArticle

An Entropic Approach for Pair Trading

by Daisuke Yoshikawa

Entropy 2017, 19(7), 320; https://doi.org/10.3390/e19070320 - 30 Jun 2017

Cited by 3 | Viewed by 5132

Abstract

In this paper, we derive the optimal boundary for pair trading. This boundary defines the points of entry into or exit from the market for a given stock pair. However, if the assumed model contains uncertainty, the resulting boundary could result in large [...] Read more.

In this paper, we derive the optimal boundary for pair trading. This boundary defines the points of entry into or exit from the market for a given stock pair. However, if the assumed model contains uncertainty, the resulting boundary could result in large losses. To avoid this, we develop a more robust strategy by accounting for the model uncertainty. To incorporate the model uncertainty, we use the relative entropy as a penalty function in the expected profit from pair trading. Full article

(This article belongs to the Special Issue Entropic Applications in Economics and Finance)

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2440 KiB

Open AccessArticle

The Entropic Linkage between Equity and Bond Market Dynamics

by Edgar Parker

Entropy 2017, 19(6), 292; https://doi.org/10.3390/e19060292 - 21 Jun 2017

Cited by 8 | Viewed by 7661

Abstract

An alternative derivation of the yield curve based on entropy or the loss of information as it is communicated through time is introduced. Given this focus on entropy growth in communication the Shannon entropy will be utilized. Additionally, Shannon entropy’s close relationship to [...] Read more.

An alternative derivation of the yield curve based on entropy or the loss of information as it is communicated through time is introduced. Given this focus on entropy growth in communication the Shannon entropy will be utilized. Additionally, Shannon entropy’s close relationship to the Kullback–Leibler divergence is used to provide a more precise understanding of this new yield curve. The derivation of the entropic yield curve is completed with the use of the Burnashev reliability function which serves as a weighting between the true and error distributions. The deep connections between the entropic yield curve and the popular Nelson–Siegel specification are also examined. Finally, this entropically derived yield curve is used to provide an estimate of the economy’s implied information processing ratio. This information theoretic ratio offers a new causal link between bond and equity markets, and is a valuable new tool for the modeling and prediction of stock market behavior. Full article

(This article belongs to the Special Issue Entropic Applications in Economics and Finance)

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3276 KiB

Open AccessArticle

Structural Correlations in the Italian Overnight Money Market: An Analysis Based on Network Configuration Models

by Duc Thi Luu, Thomas Lux and Boyan Yanovski

Entropy 2017, 19(6), 259; https://doi.org/10.3390/e19060259 - 06 Jun 2017

Cited by 3 | Viewed by 4745

Abstract

We study the structural correlations in the Italian overnight money market over the period 1999–2010. We show that the structural correlations vary across different versions of the network. Moreover, we employ different configuration models and examine whether higher-level characteristics of the observed network [...] Read more.

We study the structural correlations in the Italian overnight money market over the period 1999–2010. We show that the structural correlations vary across different versions of the network. Moreover, we employ different configuration models and examine whether higher-level characteristics of the observed network can be statistically reconstructed by maximizing the entropy of a randomized ensemble of networks restricted only by the lower-order features of the observed network. We find that often many of the high order correlations in the observed network can be considered emergent from the information embedded in the degree sequence in the binary version and in both the degree and strength sequences in the weighted version. However, this information is not enough to allow the models to account for all the patterns in the observed higher order structural correlations. In particular, one of the main features of the observed network that remains unexplained is the abnormally high level of weighted clustering in the years preceding the crisis, i.e., the huge increase in various indirect exposures generated via more intensive interbank credit links. Full article

(This article belongs to the Special Issue Entropic Applications in Economics and Finance)

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351 KiB

Open AccessArticle

The Tale of Two Financial Crises: An Entropic Perspective

by Ramazan Gençay and Nikola Gradojevic

Entropy 2017, 19(6), 244; https://doi.org/10.3390/e19060244 - 24 May 2017

Cited by 21 | Viewed by 5958

Abstract

This paper provides a comparative analysis of stock market dynamics of the 1987 and 2008 financial crises and discusses the extent to which risk management measures based on entropy can be successful in predicting aggregate market expectations. We find that the Tsallis entropy [...] Read more.

This paper provides a comparative analysis of stock market dynamics of the 1987 and 2008 financial crises and discusses the extent to which risk management measures based on entropy can be successful in predicting aggregate market expectations. We find that the Tsallis entropy is more appropriate for the short and sudden market crash of 1987, while the approximate entropy is the dominant predictor of the prolonged, fundamental crisis of 2008. We conclude by suggesting the use of entropy as a market sentiment indicator in technical analysis. Full article

(This article belongs to the Special Issue Entropic Applications in Economics and Finance)

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348 KiB

Open AccessArticle

Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory

by Henryk Gzyl and Silvia Mayoral

Entropy 2017, 19(4), 153; https://doi.org/10.3390/e19040153 - 01 Apr 2017

Cited by 1 | Viewed by 3485

Abstract

Here, we consider the following inverse problem: Determination of an increasing continuous function

U (x)

on an interval

[a, b]

from the knowledge of the integrals [...] Read more.

Here, we consider the following inverse problem: Determination of an increasing continuous function

U (x)

on an interval

[a, b]

from the knowledge of the integrals

\int U (x) d F_{X_{i}} (x) = π_{i}

where the

X_{i}

are random variables taking values on

[a, b]

and

π_{i}

are given numbers. This is a linear integral equation with discrete data, which can be transformed into a generalized moment problem when

U (x)

is supposed to have a positive derivative, and it becomes a classical interpolation problem if the

X_{i}

are deterministic. In some cases, e.g., in utility theory in economics, natural growth and convexity constraints are required on the function, which makes the inverse problem more interesting. Not only that, the data may be provided in intervals and/or measured up to an additive error. It is the purpose of this work to show how the standard method of maximum entropy, as well as the method of maximum entropy in the mean, provides an efficient method to deal with these problems. Full article

(This article belongs to the Special Issue Entropic Applications in Economics and Finance)

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Review

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5389 KiB

Open AccessReview

Economics and Finance: q-Statistical Stylized Features Galore

by Constantino Tsallis

Entropy 2017, 19(9), 457; https://doi.org/10.3390/e19090457 - 31 Aug 2017

Cited by 32 | Viewed by 6199

Abstract

The Boltzmann–Gibbs (BG) entropy and its associated statistical mechanics were generalized, three decades ago, on the basis of the nonadditive entropy

S_{q}

(

q \in R

), which recovers the BG entropy in the

q \to 1

limit. The optimization of [...] Read more.

The Boltzmann–Gibbs (BG) entropy and its associated statistical mechanics were generalized, three decades ago, on the basis of the nonadditive entropy

S_{q}

(

q \in R

), which recovers the BG entropy in the

q \to 1

limit. The optimization of

S_{q}

under appropriate simple constraints straightforwardly yields the so-called q-exponential and q-Gaussian distributions, respectively generalizing the exponential and Gaussian ones, recovered for

q = 1

. These generalized functions ubiquitously emerge in complex systems, especially as economic and financial stylized features. These include price returns and volumes distributions, inter-occurrence times, characterization of wealth distributions and associated inequalities, among others. Here, we briefly review the basic concepts of this q-statistical generalization and focus on its rapidly growing applications in economics and finance. Full article

(This article belongs to the Special Issue Entropic Applications in Economics and Finance)

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