Investment Irreversibility and Finance Constraints

This paper analyses the investment behaviour of firms in the presence of irreversibility and of a dividend payout constraint. Estimation of investment equations for a panel of UK firms shows that the Q model performs well, over regions of the sample space, where neither constraint is likely to be binding. The constraints are able to account for the empirical significance of cash flow variables for the remaining firms in the sample.     

Ordering univariate distributions by entropy and variance

This paper examines the role of variance and entropy in ordering distributions and random prospects. There is no universal relation between entropy and variance orderings of distributions. But we place their relationship in the context of a stronger ordering relation known as dispersion ordering. Further, some conditions are identified under which variance and entropy order similarly when continuous variables are transformed. We also analyze parametric changes which do not disturb the agreement between these rankings. The results are conveniently tabulated in terms of distribution parameters.     

Generalized cumulative residual entropy and record values

The Shannon entropy of a random variable has become a very useful tool in Probability Theory. In this paper we extend the concept of cumulative residual entropy introduced by Rao et al. (in IEEE Trans Inf Theory 50:1220–1228, 2004). The new concept called generalized cumulative residual entropy (GCRE) is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. We also consider a dynamic GCRE obtained using the residual lifetime. For these concepts we obtain some characterization results, stochastic ordering and aging classes properties and some relationships with other entropy concepts.     

The method of entropy maximization

Use of Boltzmann’sH-function has been widely advocated for the «production», via its maximization under constraints, of prior probability distributions, e.g. in the search for noninformative priors in econometrics. The procedure appears to rest on a misunderstanding of theH-function’s role in statistical mechanics, where it was first introduced by Boltzmann. This paper traces the origin and development of the method and criticizes its inappropriate and misleading applications.     

Relative entropy in sequential decision problems

Consider an agent who faces a sequential decision problem. At each stage the agent takes an action and observes a stochastic outcome (e.g., daily prices, weather conditions, opponents' actions in a repeated game, etc.). The agent's stage-utility depends on his action, the observed outcome and on previous outcomes. We assume the agent is Bayesian and is endowed with a subjective belief over the distribution of outcomes. The agent's initial belief is typically inaccurate. Therefore, his subjectively optimal strategy is initially suboptimal. As time passes information about the true dynamics is accumulated and, depending on the compatibility of the belief with respect to the truth, the agent may eventually learn to optimize. We introduce the notion of relative entropy, which is a natural adaptation of the entropy of a stochastic process to the subjective set-up. We present conditions, expressed in terms of relative entropy, that determine whether the agent will eventually learn to optimize. It is shown that low entropy yields asymptotic optimal behavior. In addition, we present a notion of pointwise merging and link it with relative entropy.     

Some results on residual entropy function

Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the Shannon residual entropy function as a useful dynamic measure of uncertainty. They studied the characterization problem from the residual entropy. They also used this function to define a stochastic order and two classes of distributions, DURL and IURL. In this paper, we obtain some new results on this function and we correct some mistakes in the preceding literature.Supported by Ministerio de Ciencia y Tecnologia under grant BFM2000-0362Acknowledgements. We thank two anonymous referees for some useful comments that led to an improvement in the presentation of this paper.     

Maximum entropy autoregressive conditional heteroskedasticity model

In many applications, it has been found that the autoregressive conditional heteroskedasticity (ARCH) model under the conditional normal or Student’s t distributions are not general enough to account for the excess kurtosis in the data. Moreover, asymmetry in the financial data is rarely modeled in a systematic way. In this paper, we suggest a general density function based on the maximum entropy (ME) approach that takes account of asymmetry, excess kurtosis and also of high peakedness. The ME principle is based on the efficient use of available information, and as is well known, many of the standard family of distributions can be derived from the ME approach. We demonstrate how we can extract information functional from the data in the form of moment functions. We also propose a test procedure for selecting appropriate moment functions. Our procedure is illustrated with an application to the NYSE stock returns. The empirical results reveal that the ME approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively.     

Equivalence between welfare and entropy approaches to residential location

An optimization model for residential location in an urban area is presented. As the objective, a welfare measure is considered which is derived as aggregated expected utility based on utility-maximizing individual behaviour. The utilities include travel costs for work trips as well as a measure of the disutility with high-density living. The problem of finding a welfare maximizing housing allocation is shown to be equivalent to an entropy maximizing problem provided that a certain condition is met. By considering a dual formulation, a computationally more expedient problem is obtained. The model approach is illustrated by a few applications to the Stockholm region.     

The entropy paradox and the distribution of urban population

This paper presents an empirical application of an information theoretic approach to spatial hypothesis testing. Following the lead of Batty [1] this study employs the concept of expected information to test hypotheses concerning the distribution of urban population and population density in San Antonio for the years 1960 and 1970. Cast for the first time in a longitudinal context, major concerns of this work are the relative advantages, both theoretical and methodological, of certain entropy measures. Specifically, comparisons are made between the Shannon and the Kullback formulations. In this context of comparison, problems closely linked to what has been called the “entropy paradox” are identified and explained, suggesting important qualitative differences between these two measures.     

房地产开发项目投资组合的均值——信息熵模型

以方差作为风险度量指标存在着计算复杂、计算结果不稳定等缺陷,本文并将信息熵度量风险的方法引入房地产开发项目投资组合中,建立了房地产投资组合的均值-信息熵模型。实例证明,该模型计算简单,具有较强的有效性和实用性。     

房地产开发项目投资组合的均值--信息熵模型

以方盖作为风险度量指标存在着计算复杂、计算结果不稳定等缺陷,本文并将信息熵度量风险的方法引入房地产开发项目投资组合中,建立了房地产投资组合的均值-信息熵模型.实例证明,该模型计算简单,具有较强的有效性和实用性.     

熵变:企业并购的动因分析

本文简要地评述了国内外学者对企业并购的理论与应用文献。在前辈们的基础上,文章从企业的管理性质——耗散结构入手,解析了企业并购的动因是追求企业的熵变为负。在熵变为负的情况下,企业向社会输入负熵,社会支持企业回报负熵,两者在组成一个开放系统的基础下,达到双赢。     

A non-parametric independence test using permutation entropy

In the present paper we construct a new, simple, consistent and powerful test for independence by using symbolic dynamics and permutation entropy as a measure of serial dependence. We also give a standard asymptotic distribution of an affine transformation of the permutation entropy under the null hypothesis of independence. The test statistic and its standard limit distribution are invariant to any monotonic transformation. The test applies to time series with discrete or continuous distributions. Eventhough the test is based on entropy measures, it avoids smoothed non-parametric estimation. An application to several daily financial time series illustrates our approach.     

Sharp exponential and entropy bounds on expectations of generalized order statistics

Sharp lower and upper bounds on expected values of generalized order statistics are proven by the use of Moriguti's inequality combined with the Young inequality. The bounds are expressed in terms of exponential moments or entropy. They are attainable providing new characterizations of some nontrivial distributions. Received October 2001/Revised May 2002     

On some functional equations concerning entropy,directed divergence and inaccuracy

This paper deals with the characterizations of some measures of entropy, inaccuracy and directed—divergence by means of functional equations.     

熵的本质与投资风险的度量

在一些关于风险决策模型的文献中,使用熵作为风险的度量。本文从熵的本质出发,结合举例和原理分析,指出其中存在的不合理性,并对风险的度量和熵在决策中的应用进行了一些阐述。     

Efficient frontier estimation: a maximum entropy approach

An alternative efficiency estimation approach is developed utilizing generalized maximum entropy (GME). GME combines the strengths of both SFA and DEA, allowing for the estimation of a frontier that is stochastic, without making an ad hoc assumption about the distribution of the efficiency component. GME results approach SFA results as the one-sided inefficiency bounds used by GME shrink. Results similar to DEA are achieved as the bounds increase. The GME results are distributed like DEA, but yield virtually the same rankings as SFA. The results suggest that GME may provide a link between various estimators of efficiency.