Extendible stock loan

In this paper, the model of extendible stock loan with forbearance is proposed. The loan is extendible, so as to prevent immediate losses or to prevent subsequent price drop; while the forbearance is granted only when the pledged share’s value is above threshold, so as to mitigate the risk-taking behavior induced by the extension. The non-synchronization of the liquidation of insolvent stock loans also alleviates the downward leverage spiral in a market downturn. Numerical analysis shows that fair extendible stock loan rates increase with the forbearance level as well as extension period, and loan rates are quite sensitive to the change of asset volatility and debt ratio. For lenders waiving the interest rates during extension period, their burden grows with extension rapidly when they grant looser forbearance and when asset volatility or loan-to-value is higher. Some suggestions are made accordingly. First, lenders offering uniform extendible loan rate can let borrowers choose between looser forbearance with shorter extension, or tighter forbearance with longer extension. Second, if the loan rate is priced fairly, lower margin requirement can only be accomplished with tighter forbearance. More looser forbearance worth higher rates.     

随机数在随机事件与概率教学中的应用探索

本文对在随机事件与概率中的常见问题提出了一种新的借助于计算机实现的解决思路,即通过机器自动产生随机数后构建相应的数学模型,再通过编程计算得到最后结果。该方法既为概率论的教学带来了创新性思维,也为当前的教师提出了新的挑战。     

A barrier options approach to modeling project failure: The case of hydrogen fuel infrastructure

Hydrogen fuel cell vehicles have the potential to contribute to a sustainable transport system with zero tailpipe emissions. This requires the construction of a network of fuel stations, a long-term, expensive and highly uncertain investment. We contribute to the literature by including a knock-out barrier option in an n-fold compound real option model to take account of immediate project failure in a multi-stage sequential investment project. Our model allows to explicitly incorporate the default possibility of large-scale energy infrastructure projects. In our case study of hydrogen infrastructure development, we find that even for the least conservative valuation method no profitable business case can be made for the development of hydrogen as a sustainable transportation mode. However, we do provide some suggestive scenarios that plausible tax schedules can be designed to overcome the starting problems for hydrogen infrastructure development.     

Students' Characteristics and Performance in Economic Statistics

The vast majority of studies in college economics have dealt with the introductory principles course. In one of the rare research projects dealing with other courses, Professor Cohn attempts to identify factors affecting student performance in economic statistics. He considers such variables as grade point average, graduate vs. undergraduate status, major field, sex and credits in economics, mathematics and statistics. There are a few recognized limitations to his model, but the reader will find some of his results to be surprising indeed.     

Spatial modelling of claim frequency and claim size in non-life insurance

In this paper, models for claim frequency and average claim size in non-life insurance are considered. Both covariates and spatial random effects are included allowing the modelling of a spatial dependency pattern. We assume a Poisson model for the number of claims, while claim size is modelled using a Gamma distribution. However, in contrast to the usual compound Poisson model, we allow for dependencies between claim size and claim frequency. A fully Bayesian approach is followed, parameters are estimated using Markov Chain Monte Carlo (MCMC). The issue of model comparison is thoroughly addressed. Besides the deviance information criterion and the predictive model choice criterion, we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. We give an application to a comprehensive data set from a German car insurance company. The inclusion of spatial effects significantly improves the models for both claim frequency and claim size, and also leads to more accurate predictions of the total claim sizes. Further, we detect significant dependencies between the number of claims and claim size. Both spatial and number of claims effects are interpreted and quantified from an actuarial point of view.     

Optimal reinsurance under general law-invariant risk measures

In recent years, general risk measures play an important role in risk management in both finance and insurance industry. As a consequence, there is an increasing number of research on optimal reinsurance decision problems using risk measures beyond the classical expected utility framework. In this paper, we first show that the stop-loss reinsurance is an optimal contract under law-invariant convex risk measures via a new simple geometric argument. A similar approach is then used to tackle the same optimal reinsurance problem under Value at Risk and Conditional Tail Expectation; it is interesting to note that, instead of stop-loss reinsurances, insurance layers serve as the optimal solution. These two results highlight that law-invariant convex risk measure is better and more robust, in the sense that the corresponding optimal reinsurance still provides the protection coverage against extreme loss irrespective to the potential increment of its probability of occurrence, to expected larger claim than Value at Risk and Conditional Tail Expectation which are more commonly used. Several illustrative examples will be provided.     

等比级数在函数展开成幂级数中的应用

函数的幂级数展开是高等数学的教学重点之一,在解决函数的幂级数展开的问题中,等比级数起着重要的作用。文章介绍了利用等比级数将函数展开成幂级数的常见情形,并给出了具体的例子。     

Moments of Compound Mixed Poisson Distributions

Recursive formulae are derived for the evaluation of the moments and the descending factorial moments about a point n of mixed Poisson and compound mixed Poisson distributions, in the case where the derivative of the logarithm of the mixing density can be written as a ratio of polynomials. As byproduct, we also obtain recursive formulae for the evaluation of the moments about the origin, central moments, descending and ascending factorial moments of these distributions. Examples are also presented for a number of mixing densities.     

数字化成图软件在公路线形设计上的应用研究

本文试图通过对地形、地籍数字化成图软件功能的改进,包括公路线形设计、纵横断面图的绘制和设计、土石方的计算与调配,以及各种数据表格的自动输出等,实现操作轻松快捷、简单准确,满足公路设计单位的需要,提高工作效率。     

一类新的反Smarandache几何级数周期行列式

本文定义了一类新的反Smarandache几何级数周期行列式,并利用初等数论的方法和行列式的性质,对这类行列式进行了研究,给出了它们的通项公式。