The synchronization club: classification of global economic groups by inequality

We find that, from 1970 to 2006, the GDPs of 181 countries are described by a log-normal with a power law tail before 1992, but by a kinked power law distribution after 1992. In the 15 years from 1992 to 2006, there are two obvious scale-free zones for annual GDPs, ranked from the largest to smallest. If the countries in each scaling region are regarded as a group, the world is divided into two groups, each with a roughly stable number of members. The power exponents of the two groups are different and hence lead to different inequalities. Therefore, the basis for classification is the macro-consistent inequality within each group. The wealth grows in a synchronous nonlinear manner within groups that have a stable wealth distribution and rank structure. If each group is considered as a club, we name it a ‘synchronization club’.     

Reflections on the Structure and Origin of Pareto Income Distributions

The essay takes the reader on a voyage of exploration with the aim of discovering the origin of Pareto-curves. It shows with thought-experiments backed up by computer-simulation the generation of log-normal curves in detail. Extending forward this conceptual trajectory, it arrives via a quasi-Newtonian fluxion-insight – infinitessimal differential integration – at a novel mathematical concept: Pareto-curves are simply special log-normal curves where a large number of random-factors interacted and impacted at their genesis (the author called it the Kopp-effect).     

Pricing of Defaultable Bonds with Log-Normal Spread: Development of the Model and an Application to Argentinean and Brazilian Bonds During the Argentine Crisis

In this paper we describe a two-factor model for a defaultable discount bond, assuming log-normal dynamics with bounded volatility for the instantaneous short rate spread. Under some simplified hypothesis, we obtain an explicit barrier-type solution for zero recovery and constant recovery. We also present a numerical application for Argentinean and Brazilian Sovereign Bonds during the default crisis of Argentina.JEL Classification: G 13     

An empirical re-examination of extreme tail behavior: testing the assumptions of the power laws and the generalized Pareto distribution on the financial series

This study investigates whether the power laws and the associated generalized Pareto distribution (GPD) exist in the extreme tail behavior of financial return series. We include 10 series of five major financial categories over the period 1971–2018 for empirical analysis. For the former assumption, we test three representative power-law distributions. For the latter, we employ an innovative bootstrap goodness-of-fit test of GPD modeling. We also discuss the relationship between both assumptions. The empirical outcomes indicate that both assumptions do not necessarily hold for all tail series due to the outlying observations. The rejection of the power laws assumption leads to the rejection of the GPD assumption. This rejection does not promise the non-rejection of power laws either. However, the non-rejection of either assumption does not imply non-rejection of the other assumption. Power-law distribution and exponential distribution outperform log-normal distribution in tail fitting. GPD fits better at the 1% quantile level than at the 5% level. Overall, we need to acknowledge the considerable gap between the goodness-of-fit testing outcomes of both the power laws and GPD assumptions.     

Generalized log-normal chain-ladder

ABSTRACT

We propose an asymptotic theory for distribution forecasting from the log-normal chain-ladder model. The theory overcomes the difficulty of convoluting log-normal variables and takes estimation error into account. The results differ from that of the over-dispersed Poisson model and from the chain-ladder-based bootstrap. We embed the log-normal chain-ladder model in a class of infinitely divisible distributions called the generalized log-normal chain-ladder model. The asymptotic theory uses small σ asymptotics where the dimension of the reserving triangle is kept fixed while the standard deviation is assumed to decrease. The resulting asymptotic forecast distributions follow t distributions. The theory is supported by simulations and an empirical application.     

我国上市公司偿债能力指标的分布特征研究

通过对上海证券交易所2004年上市公司年报的4个财务比率指标的统计分析,发现表征短期偿债能力的财务比率指标服从对数正态分布,表征长期偿债能力的财务指标服从正态分布。另外,对近几年上市公司年报的数据进行统计分析,证实短期偿债指标和长期偿债指标的分布特征表现相对稳定,这同时也说明我国上市公司整体上偿债能力表现比较稳定,波动不是很大。     

The geometric chain-ladder

Abstract

The log normal reserving model is considered. The contribution of the paper is to derive explicit expressions for the maximum likelihood estimators. These are expressed in terms of development factors which are geometric averages. The distribution of the estimators is derived. It is shown that the analysis is invariant to traditional measures for exposure.     

Determining the Optimum Process Mean under a Log-normal Distribution

Wen and Mergen [Quality Engineering (1999) vol. 11, pp. 505–509] used the unbalanced step loss function for measuring the cost of the nonconforming item and adopted a trade-off model for determining the optimum process mean. They assumed that the quality characteristic is normally distributed, the process variance is constant, and the process mean is unknown. In this paper, we further present the modified Wen and Mergens (1999) model with log-normal distribution. The step loss function and the piecewise linear loss function of product are considered in the modified model.