A note on “Modelling exchange rate returns: which flexible distribution to use?”

Corlu and Corlu [Quant. Finance, 2014, doi: 10.1080/14697688.2014.942231] provided a novel modelling of exchange rate data for nine currencies using five flexible distributions. They stated that the generalized lambda, skew t and normal inverse Gaussian distributions ‘do a good job’. Here, we reanalyse the data and show that a distribution simpler than all of these fits at least as well as these distributions. We also find that the normal inverse Gaussian distribution provides good fits for only one of the data-sets.     

Confined exponential approximations for the valuation of American options

We provide an alternative analytic approximation for the value of an American option using a confined exponential distribution with tight upper bounds. This is an extension of the Geske and Johnson compound option approach and the Ho et al. exponential extrapolation method. Use of a perpetual American put value, and then a European put with high input volatility is suggested in order to provide a tighter upper bound for an American put price than simply the exercise price. Numerical results show that the new method not only overcomes the deficiencies in existing two-point extrapolation methods for long-term options but also further improves pricing accuracy for short-term options, which may substitute adequately for numerical solutions. As an extension, an analytic approximation is presented for a two-factor American call option.     

电网企业优化购电成本方法研究与实证分析

通过购电成本结构分析,指出了当前发电计划编制及执行中存在的问题和当前发电计划编制对电网购电费的影响。重点研究了有关降低电网购电成本的方法及实证,并为政府价格相关部门提出创建节能型社会的政策建议。     

大型沉管管节浮运航道适航特性建模分析

为确保沉管隧道在航道中长期浮运作业的安全性与可靠性,依托深中通道工程备选预制厂方案,建立珠江口局部区域二维水流数学模型,在实测水文资料验证的基础上,通过模型计算揭示了浮运航道的水动力变化特征,开展航道范围内横流、纵流的变化特点分析.分析结果表明:工程实施后,龙穴港池水域的潮流流速普遍较弱,南沙四期港池水域流速变化较小,...     

Compound mixed Poisson distributions I

The concept of compound mixed Poisson distributions in actuarial science is used to represent such variables as the total amount of claims or losses payable by an insurer. In this paper, comprehensive collections of approximate forms are derived for the compound mixed Poisson distribution. The calculations involve use of several special functions and their properties. We believe that the results will serve as an important reference in actuarial science.     

On composite lognormal-Pareto models

Recently, Cooray & Ananda (2005) proposed a composite lognormal-Pareto model for use with loss payments data of the sort arising in the actuarial and insurance industries. Their model is based on a lognormal density up to an unknown threshold value and a two-parameter Pareto density thereafter. Here we identify and discuss limitations of this composite lognormal-Pareto model which are likely to severely curtail its potential for practical application to real world data sets. In addition, we present two different composite models based on lognormal and Pareto models in order to address these concerns. The performance of all three composite models is discussed and compared in the context of an example based upon a well-known fire insurance data set.     

Mean and dispersion modelling for policy claims costs

A model for the statistical analysis of the total amount of insurance paid out on a policy is developed and applied. The model simultaneously deals with the number of claims (zero or more) and the amount of each claim. The number of claims is from a Poisson-based discrete distribution. Individual claim sizes are from a continuous right skewed distribution. The resulting distribution of total claim size is a mixed discrete-continuous model, with positive probability of a zero claim. The means and dispersions of the claim frequency and claim size distribution are modeled in terms of risk factors. The model is applied to a car insurance data set.     

On a rank-order test for the equality of probability of an event

Abstract

The following situation is considered. A fixed number (= n) or sequence of independent trials T ₁ T ₂,…, T _n is given, and in each of these an event E mayor may not occur, It is further observed that the event E occurs a total of k times amongst the n trials T _i , (i = l,…, n). It is then required to test the hypothesis H ₀ that the probability of the occurrence of E is constant from trial to trial, i.e. H ₀ is the hypothesis: p ₁ = p ₂ = ? = p _n = p, if p _n (i = 1, …, n) represents the probability that E occurs on the ith trial.     

Improved approximations for the aggregate claims distribution of a life insurance portfolio

Abstract

In an earlier paper the author derived a recursion formula which permits the exact computation of the aggregrate claims distribution in the individual life model. This exact procedure requires of course more computing time than approximative methods such as Kornya's algorithm, which seemed to be the best compromise between accuracy and computational effort. In the present paper it is shown that, to save time, the exact formula can be used in an approximative way and that the corresponding error bound is smaller than the one of the Kornya-type approximations.     

A generalized penalty function for a class of discrete renewal processes

Analysis of a generalized Gerber–Shiu function is considered in a discrete-time (ordinary) Sparre Andersen renewal risk process with time-dependent claim sizes. The results are then applied to obtain ruin-related quantities under some renewal risk processes assuming specific interclaim distributions such as a discrete K _n distribution and a truncated geometric distribution (i.e. compound binomial process). Furthermore, the discrete delayed renewal risk process is considered and results related to the ordinary process are derived as well.