Pricing of a structured product on the SX5E when the uncertainty of returns is modeled as a log-stable process

This work presents the participation factor and the valuation of a first-generation structured product with European call options on the Eurostoxx, when the uncertainty of the yields is modeled through log-stable processes. The basic statistics of the index yields are also exposed, the α-stable parameters are estimated, and the valuation of the of the structured models is compared through the log-stable and log-Gaussian models using inputs from the bond markets; concluding that investors obtain higher yields than those of the bond market through both models, and that the differences of the yields depend on the participation factor and on the value of the index at the time of liquidation.     

THE BIVARIATE EXPONENTIAL DISTRIBUTION; A REVIEW AND SOME NEW RESULTS

Various models have been proposed as bivariate forms of the exponential distribution. A brief but comprehensive review is presented which classifies, interrelates and contrasts the different models and outlines what is known about distributional properties, applicability and estimation and testing of parameters (particularly the association parameter). Some new results are presented for one particular model. Maximum likelihood, and moment–type, estimators of the association parameter are examined. Asymptotic variances are derived and attention is given to the relative efficiency of the estimators and to problems of their evaluation.     

Limit theorems for multivariate discrete distributions

According to the usual law of small numbers a multivariate Poisson distribution is derived by defining an appropriate model for multivariate Binomial distributions and examining their behaviour for large numbers of trials and small probabilities of marginal and simultaneous successes. The weak limit law is a generalization of Poisson's distribution to larger finite dimensions with arbitrary dependence structure. Compounding this multivariate Poisson distribution by a Gamma distribution results in a multivariate Pascal distribution which is again asymptotically multivariate Poisson. These Pascal distributions contain a class of multivariate geometric distributions. Finally the bivariate Binomial distribution is shown to be the limit law of appropriate bivariate hypergeometric distributions. Proving the limit theorems mentioned here as well as understanding the corresponding limit distributions becomes feasible by using probability generating functions.     

广义三棱柱地质模型的工程应用

采用广义三棱柱地质模型,实现工程地质的三维可视化,可以帮助工程人员迅速地掌握工程地质情况。     

Closed-form Bayesian inferences for the logit model via polynomial expansions

Articles in Marketing and choice literatures have demonstrated the need for incorporating person-level heterogeneity into behavioral models (e.g., logit models for multiple binary outcomes as studied here). However, the logit likelihood extended with a population distribution of heterogeneity doesn’t yield closed-form inferences, and therefore numerical integration techniques are relied upon (e.g., MCMC methods). We present here an alternative, closed-form Bayesian inferences for the logit model, which we obtain by approximating the logit likelihood via a polynomial expansion, and then positing a distribution of heterogeneity from a flexible family that is now conjugate and integrable. For problems where the response coefficients are independent, choosing the Gamma distribution leads to rapidly convergent closed-form expansions; if there are correlations among the coefficients one can still obtain rapidly convergent closed-form expansions by positing a distribution of heterogeneity from a Multivariate Gamma distribution. The solution then comes from the moment generating function of the Multivariate Gamma distribution or in general from the multivariate heterogeneity distribution assumed. Closed-form Bayesian inferences, derivatives (useful for elasticity calculations), population distribution parameter estimates (useful for summarization) and starting values (useful for complicated algorithms) are hence directly available. Two simulation studies demonstrate the efficacy of our approach. JEL Classification C6 · C8 · M3     

Estimating Discrete Joint Probability Distributions for Demographic Characteristics at the Store Level Given Store Level Marginal Distributions and a City-Wide Joint Distribution

This paper provides a solution to the problem of estimating a joint distribution using the associated marginal distributions and a related joint distribution. The particular application we have in mind is estimating joint distributions of demographic characteristics corresponding to market areas for individual retail stores. Marginal distributions are generally available at the census tract level, but joint distributions are only available for Metropolitan Statistical Areas which are generally much larger than the market for a single retail store. Joint distributions over demographics are an important input into mixed logit demand models for aggregate data. Market shares that vary systematically with demographics are essential for relieving the restrictions imposed by the Independence from Irrelevant Alternative property of the logit model.We approach this problem by formulating a parametric function that incorporates both the city-wide joint distributional information and marginal information specific to the retail stores market area. To estimate the function, we form moment conditions equating the moments of the parametric function to observed data, and we input these into a GMM objective. In one of our illustrations we use four marginal demographic distributions from each of eight stores in Dominicks Finer Foods data archive to estimate a four dimensional joint distribution for each store. Our results show that our GMM approach produces estimated joint distributions that differ substantially from the product of marginal distributions and emit marginals that closely match the observed marginal distributions. Mixed logit demand estimates are also presented which show the estimates to be sensitive to the formulation of the demographics distribution.The views expressed are not purported to reflect those of the United States Department of Justice     

基于MF-DFA的中国股指期货价格的多重分形实证研究

本文通过应用多重分形谱分析法和多重分形消除趋势波动分析（MF-DFA）法,研究了新产生的中国股指期货市场的多重分形性。通过对2942个股指期货最后十分钟结算价格的分析,我们发现中国股指期货的收益率具有长程相关性和多重分形性,期货价格波动并不能用单一的标度指数进行充分描述。进一步通过将原始序列和转换后的收益序列进行比较,转换过程包括重排以及相位随机化,我们发现导致中国股指期货市场多重分形性的两种不同成因。研究结果表明,虽然厚尾分布是造成多重分形性的一个方面,但长程相关性才是引起中国股指期货市场多重分形的主要原因。     

Unconditional distributions obtained from conditional specification models with applications in risk theory

Bivariate distributions, specified in terms of their conditional distributions, provide a powerful tool to obtain flexible distributions. These distributions play an important role in specifying the conjugate prior in certain multi-parameter Bayesian settings. In this paper, the conditional specification technique is applied to look for more flexible distributions than the traditional ones used in the actuarial literature, as the Poisson, negative binomial and others. The new specification draws inferences about parameters of interest in problems appearing in actuarial statistics. Two unconditional (discrete) distributions obtained are studied and used in the collective risk model to compute the right-tail probability of the aggregate claim size distribution. Comparisons with the compound Poisson and compound negative binomial are made.     

Poverty Orderings

This paper reviews the literature of partial poverty orderings. Partial poverty orderings require unanimous poverty rankings for a class of poverty measures or a set of poverty lines. The need to consider multiple poverty measures and multiple poverty lines arises inevitably from the arbitrariness inherent in poverty comparisons. In the paper, we first survey the ordering conditions of various individual poverty measures for a range of poverty lines; for some measures necessary and sufficient conditions are identified while for others only some easily verifiable sufficient conditions are established. These ordering conditions are shown to have a close link with the stochastic dominance relations which are based on the comparisons of cumulative distribution functions. We then survey the ordering conditions for various classes of poverty measures with a single or a set of poverty lines; in all cases necessary and sufficient conditions are established. These conditions again rely on the stochastic dominance relations or their transformations. We also extend the relationship between poverty orderings and stochastic dominance to higher orders and explore the possibility and the conditions of increasing the power of poverty orderings beyond the second degree dominance condition.     

双曲拱桥病害分析及加固改造

通过对湖南干线公路几座双曲拱桥的检测评估实践,文章介绍了双曲拱桥的主要病害及原因,并提出可行的改造加固措施。