A correlation-formula

Abstract

The late Professor T. N. THIELE has pointed out, ¹ Bulletins de l'Académie Royale de Danemark, 1906 N:o 3 p. 149–152. that a given correlation may sometimes be brought to vanish by a suitable linear transformation of the coordinates. Unfortunately his indications in this respect are very brief; and as the subject is not treated by means of frequency-surfaces, but only by a consideration of the first few moments (or rather “half-invariants ” ² A kind of rational functions of the moments, see THIELE: Theory of Ohservations, London 1903, p. 24. — The same incomplete method has heen applied by C. Burrau (Meddelelser fra den antropologiske Komite p. 243–260). ) in a particular numerical case, his efforts have not resulted in establishing a correlation-formula which alone, by comparison with the observations, could prove his assertion right or wrong. I therefore propose to resume the subject, beginning with a few remarks on frequency-distributions with one single variable, and repeating, for the sake of completeness, a certain amount of known matter.     

Über eine erweiterte Anwendung des arithmetischen Mittels und eine bemerkenswerte Beziehung mit dem Gauss'schen Exponentialgesetz

Abstract

Der wahrscheinlichste Wert einer beobachteten Grösse ist gleich dem arithmetischen Mittel aus den einzelnen Beobachtungsergebnissen. So lautet ein wichtiger Satz der Wahrscheinlichkeitstheorie, und es soll hier versucht werden, diesen Satz zu verallgemeinern. Es stellt sich nämlich die Frage, wie die Sache sich verhält, wenn die beobachtete Funktion einer Grösse sich verändert, in welcher Weise der wahrscheinliche Wert dieser Funktion durch geeignete Anwendung des arithmetischen Mittels sich berechnen lässt, und wie eine voraussetzungsfreie mechanische Ausgleichung mathematisch begründet werden kann.     

MFS货币总量测度研究及其借鉴

货币总量在一国货币政策制定和宏观经济决策方面起着重要的作用,因此,科学测度货币总量具有重要的理论价值和现实意义.文章在<货币与金融统计手册>(简称MFS)货币总量测度研究的基础上,综合评价了MFS货币总量测度方法,并结合我国国情提出科学测度货币总量的建议.     

On a renewal risk process with dependence under a Farlie–Gumbel–Morgenstern copula

In this article, we consider an extension to the renewal or Sparre Andersen risk process by introducing a dependence structure between the claim sizes and the interclaim times through a Farlie–Gumbel–Morgenstern copula proposed by Cossette et al. (2010) for the classical compound Poisson risk model. We consider that the inter-arrival times follow the Erlang(n) distribution. By studying the roots of the generalised Lundberg equation, the Laplace transform (LT) of the expected discounted penalty function is derived and a detailed analysis of the Gerber–Shiu function is given when the initial surplus is zero. It is proved that this function satisfies a defective renewal equation and its solution is given through the compound geometric tail representation of the LT of the time to ruin. Explicit expressions for the discounted joint and marginal distribution functions of the surplus prior to the time of ruin and the deficit at the time of ruin are derived. Finally, for exponential claim sizes explicit expressions and numerical examples for the ruin probability and the LT of the time to ruin are given.     

On a Sparre Andersen risk model perturbed by a spectrally negative Lévy process

In this paper, we consider a Sparre Andersen risk model perturbed by a spectrally negative Lévy process (SNLP). Assuming that the interclaim times follow a Coxian distribution, we show that the Laplace transforms and defective renewal equations for the Gerber–Shiu functions can be obtained by employing the roots of a generalized Lundberg equation. When the SNLP is a combination of a Brownian motion and a compound Poisson process with exponential jumps, explicit expressions and asymptotic formulas for the Gerber–Shiu functions are obtained for exponential claim size distribution and heavy-tailed claim size distribution, respectively.     

Some comments on the inverse problem for thinned renewal processes

Abstract

The following problem is considered: for which p ∈ (0, 1) and completely monotone functions g is g/[p+(1-p)g] completely monotone? This problem is shown to be equivalent to the inverse problem for thinned renewal processes. Some applications to gamma renewal processes are also discussed.     

不动产证券化在城市更新中的应用研究

不动产证券化被引入城市更新中具有诸多优势,这也是解决当前城市更新困境的有效途径之一。本文首先利用SWOT分析法研究不动产证券化在城市更新中的应用,然后探讨不动产证券化的最新发展类型——开发型不动产证券化的运作模式,最后对我国利用不动产证券化促进城市更新提出政策建议。     

On a risk model with dependence between interclaim arrivals and claim sizes

We consider an extension to the classical compound Poisson risk model for which the increments of the aggregate claim amount process are independent. In Albrecher and Teugels (2006 Albrecher, H. and Teugels, J. 2006. Exponential behavior in the presence of dependence in risk theory. Journal of Applied Probability, 43(1): 257–273. [Crossref], [Web of Science ®] , [Google Scholar]), an arbitrary dependence structure among the interclaim time and the subsequent claim size expressed through a copula is considered and they derived asymptotic results for both the finite and infinite-time ruin probabilities. In this paper, we consider a particular dependence structure among the interclaim time and the subsequent claim size and we derive the defective renewal equation satisfied by the expected discounted penalty function. Based on the compound geometric tail representation of the Laplace transform of the time to ruin, we also obtain an explicit expression for this Laplace transform for a large class of claim size distributions. The ruin probability being a special case of the Laplace transform of the time to ruin, explicit expressions are therefore obtained for this particular ruin related quantity. Finally, we measure the impact of the various dependence structures in the risk model on the ruin probability via the comparison of their Lundberg coefficients.     

The proper distribution function of the deficit in the delayed renewal risk model

The main focus of this paper is to extend the analysis of ruin-related quantities to the delayed renewal risk models. First, the background for the delayed renewal risk model is introduced and a general equation that is used as a framework is derived. The equation is obtained by conditioning on the first drop below the initial surplus level. Then, we consider the deficit at ruin among many random variables associated with ruin. The properties of the distribution function (DF) of the proper deficit are examined in particular.     

Buy-and-hold mean-variance portfolios with a random exit strategy

We show how buy-and-hold investors can move from horizon uncertainty to profit opportunity. The analysis is conducted under a risk-averse framework rather than the standard Markowitz formulation in the case of i.i.d. asset processes. We make this practical achievement by considering a threshold stopping rule as the strategy to determine when to exit the market. The resulting investment horizon is random and can be correlated with the market. Under this setting, we first provide an analytical approximation to optimal weights, and then identify a class of reference variables associated with the stopping rule that leads to ex-ante improvements in portfolio allocation, vis-a-vis the fixed exit time alternative. The latter conclusion is based on a generalization of the Sharpe ratio, adjusted for horizon uncertainty. The obtained investment suggestion is simple and can be implemented empirically.     

从中英两国儿童作证案例看我国证人制度的完善

本文以我国和英国儿童作证案例的对比入手,通过考量不同的证人证言处置方式,进而得出结论:英国证人制度具有完整性、系统性和实践性特征。而我国证人制度由于各方面原因,在理论和实践上都缺乏良好的基础,导致证据规则缺失,司法实践混乱,与现代证人制度相距甚远。在此基础上,笔者提出了应借鉴或参考英国经验来完善我国证人制度的三点建议:重视证人理论研究,不断加强实践运用;借鉴英国证据规则,建立证人宣誓制度;贯彻以人为本理念,完善证人保护制度。     

服务质量对品牌形象产生影响的实证分析——以中国人寿保险股份有限公司为例

本文把验证保险公司的服务质量的标准归纳为有形展示、服务可靠、服务响应、服务保证及人本服务五个方面,通过实证分析的方法检验了这五个方面测量内容的可信度,并利用从客户问卷调查结果得到的数据进行统计分析,证明这五个方面反映出的服务质量与公司品牌形象有正相关性,其中服务可靠对于寿险企业品牌形象影响最大,其他依次为服务响应、人本服务、服务保证和有形展示。