Convolution of uniform distributions and ruin probability

Abstract

This paper presents an “operational calculus” method for evaluating the convolution of uniform distributions and applies it to solve a problem in ruin theory.     

On a family of counting distributions and recursions for related compound distributions

Abstract

This paper considers a family of counting distributions whose densities satisfy certain second order difference equations. Recursions for the evaluation of related compound distributions are developed in the case of severity distributions which are concentrated on the non-negative integers. From these a characterization of the considered counting distributions is obtained, and it is shown that most of these are compound Poisson distributions.     

On asymptotic properties of an estimate of a functional of a probability density

Abstract

Bhattacharyya & Roussas (1969) proposed to estimate the functional Δ = ∫ _?∞/^∞ f ²(x)dx by , where is a kernel estimate of the probability density f(x). Schuster (1974) proposed, alternatively, to estimate Δ by , where F _n (x) is the sample distribution function, and showed that the two estimates attain the same rate of strong convergence to Δ. In this note, two large sample properties of are presented, first strong convergence of to Δ is established under less assumptions than those of Schuster (1974), and second the asymptotic normality of established.     

On the solution of a functional equation concerning mortality formulae

Abstract

1. If (x) and (y) are lives whose remaining lifetimes are stochasticallyindependent, and if the mortality of each of the lives is given by a Makeham expression, then as a well known fact (see e.g. P. F. Hooker & L. H. Longley-Cook, Life and Other Contingencies, Cambridge 1957, vol. II, pp. 137&138) the evaluation of joint-life endowments and joint-life annuities on the lives (x) and (y) may be performed by substituting a single life (u) for (x) and (y) and altering the force of interest, provided that and with the same value of the parameter c( > 1).     

The modified mixture of distributions model: a revisit

Andersen (J Financ 51, 169–204 (1996)) introduced a modification of the mixture of distributions model based on microstructure arguments. Based on a small sample of five stocks, he infers that this modified mixture of distributions (MMD) model adequately captures the joint behavior of trading volume and volatility. We re-examine this claim using a larger sample of twenty-two stocks and two sample periods. Our tests show that 59% of the sample rejects the MMD model in the period 1973–1991, the same period studied by Andersen. Results for the second period (1993–1999) are more supportive of the MMD, especially for number of trades, although nearly one-third of the sample still rejects the MMD. We conclude that further tests are needed before the general validity of the MMD can be established. JEL Classification Numbers C12, C52     

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.     

On distributions of functions of samples from a normally distributed infinite population

Abstract

7. The joint distribution of the moments a ₁₁, a ₂₂,…, a_nn and a ₁₂, …, a _1n may be deduced explicitly in the case, in which the variates χ₁, …, χ _n in (1) are mutually uncorrelated. In this case we have for the population values of the moments: α_μv = 0 for μ ═ v and, consequently, A_μv = 0 for μ ═ v, so that according to (6) λ_μv = 0 for μ ═ v; the distribution (5) of the moments α_μv is then      

On distributions of functions of samples from a normally distributed infinite population

Abstract

1. The theory of the distributions of functions of samples from a normally distributed infinite population has in recent years developed considerably, so as to comprise at present an extensive aggregate of well known distributions of functions of samples used in the practical applications of theoretical statistics, e.g. regression coefficients, total, partial and multiple correlation coefficients, total and partial standard deviations, and so on.     

Maximizing utility of consumption subject to a constraint on the probability of lifetime ruin

In this paper, we explicitly solve the problem of maximizing utility of consumption (until the minimum of bankruptcy and the time of death) with a constraint on the probability of lifetime ruin, which can be interpreted as a risk measure on the whole path of the wealth process.     

Proving regularity of the minimal probability of ruin via a game of stopping and control

We reveal an interesting convex duality relationship between two problems: (a) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and the individual can invest in a Black–Scholes financial market; (b) a controller-and-stopper problem, in which the controller controls the drift and volatility of a process in order to maximize a running reward based on that process, and the stopper chooses the time to stop the running reward and pays the controller a final amount at that time. Our primary goal is to show that the minimal probability of ruin, whose stochastic representation does not have a classical form as does the utility maximization problem (i.e., the objective’s dependence on the initial values of the state variables is implicit), is the unique classical solution of its Hamilton–Jacobi–Bellman (HJB) equation, which is a non-linear boundary-value problem. We establish our goal by exploiting the convex duality relationship between (a) and (b).     

完善金融衍生产品税制 促进金融市场健康发展

完善我国金融衍生产品税制对金融市场的健康发展有着重要意义.本文分析了我国金融衍生产品税收现状,比较了国际金融衍生产品的税收制度,并在此基础上提出要从三方面完善我国金融衍生产品税制:以法律法规形式明确金融衍生产品税收制度;降低签发和交易环节税负;完善所得环节税收制度.     

Joint Insolvency Analysis of a Shared MAP Risk Process: A Capital Allocation Application

In recent years, multivariate insurance risk processes have received increasing attention in risk theory. First-passage-time problems in the context of these insurance risk processes are of primary interest for risk management purposes. In this article we study joint-ruin problems of two risk undertakers in a proportionally shared Markovian claim arrival process. Building on the existing work in the literature, joint-ruin–related quantities are thoroughly analyzed by capitalizing on existing results in certain univariate insurance surplus processes. Finally, an application is considered where the finite-time and infinite-time joint-ruin probabilities are used as risk measures to allocate risk capital among different business lines. The proposed joint-ruin allocation principle enables us to not only capture the risk dynamics over a given time horizon, but also overcome the “cross-subsidizing” effect of many existing allocation principles.     

Random walk or a run. Market microstructure analysis of foreign exchange rate movements based on conditional probability

Using tick-by-tick data for the dollar–yen and euro–dollar exchange rates recorded on the actual transaction platform, a ‘run’—continuous increases or decreases in deal prices for the past several ticks—does have some predictable information on the direction of the next price movement. Deal price movements, that are consistent with order flows, tend to continue a run once it is started. Indeed, conditional probabilities of a run continuing in the same direction after several consecutive observations exceed 0.5. However, quote prices do not show such a run tendency. Hence, a random walk hypothesis is refuted in a simple test of a run using tick-by-tick data. In addition, a longer continuous increase of the price tends to be followed by a larger reversal. The findings suggest that those market participants who have access to real-time, tick-by-tick transaction data may have an advantage in predicting exchange rate movements. The findings reported here also lend support to the momentum trading strategy.     

Ruin probability at a given time for a model with liabilities of the fractional Brownian motion type: A partial differential equation approach

In this paper we study the ruin probability at a given time for liabilities of diffusion type, driven by fractional Brownian motion with Hurst exponent in the range (0.5, 1). Using fractional Itô calculus we derive a partial differential equation the solution of which provides the ruin probability. An analytical solution is found for this equation and the results obtained by this approach are compared with the results obtained by Monte-Carlo simulation.     

从一桩失败的中外合资经营案例谈我国对外招商引资中的失误与对策

<正> 从1979年实施对外开放至今,我国对外招商引资工作取得了卓越的成就,利用外商直接投资金额逐年上升,目前排名世界第二,仅次于美国。但是,实际利用外资金额与合同外资金额的比率不够理想,这一问题仍然困扰我国的对外招商引资工作。据统计,1979-1998年,我国实际利用外资金额(2656.03亿美元)占合同外资金额(5722.43亿美元)的比例仅为46.4％,个     

某市商业银行营业部诉正华实业总公司抵押贷款纠纷案

1995年11月26日，某市商业银行营业部与该市正华实业总公司签订了一份人民币贷款合同，合同约定：正华公司向营业部贷款500万元，月利率12．06‰，期限自1995年11月27日至1996年11月30日，具体发放时间以借据为准，同时合同还约定由正华公司将自己所有的正华大厦一至三层的使用权和转租权为该笔贷款提供抵押担保，借款合同于1995年11月27日经郑州市公证处公证。     

财政部国家税务总局联合发布《关于增值税纳税人放弃免税权有关问题的通知》

财政部和国家税务总局联合发布的《关于增值税纳税人放弃免税权有关问题的通知》(财税[2007]127号)已于2007年10月1日开始实施。该通知明确了增值税纳税人销售免税货物或劳务放弃免税权的有关问题。     

The distributions of the first and second order moments,the partial correlation coefficients and the multiple correlation coefficient in samples from a normal multivariate population

Abstract

1. When the frequency function of a statistical variable is known, one of the most important tasks of Theoretical Statistics is to find the frequency functions of some simple functions of this variable. The most important are the first and second order moments in a sample containing a certain number of values of the variable.     

财政部、国家税务总局、证监会联合发布补充通知:进一步明确个人转让上市公司限售股所得征收个人所得税的有关问题

(接上期)(二)个人发生第二条第(一)、(二)、(三)、(四)项情形、由证券机构扣缴税款的,扣缴税款的计算按照财税[2009]167号文件规定执行。纳税人申报清算时,实际转让收入按照下列原则计算:第二条第(一)项的转让收入以转让当日该股份实际转让价格计算。