Lewis' branching poisson process model from the point of view of the theory of compound poisson processes

Abstract

1. Lewis [1] has used a composite process as a model for computer failure patterns. This model seems to be of a much wider scope of application at least after some modifications, which are discussed in this note. ¹ The present author has read Lewis [1] only in the form of a galley proof with due regard to a few corrections kindly communicated by Lewis. This note was prepared in 1964 before the publication of Lewis' paper.      

The theory of confluent hypergeometric functions and its application to compound poisson processes

Abstract

A. Confluent Hypergeometric Functions

The theory of such functions will be recapitulated here following a recently published book (Slater, L. J., Confluent Hypergeometric Functions, Cambr. Univ. Press 1960).     

On the asymptotic behavior of the mixed poisson process

Abstract

The recent note by Pfeifer (1982) suggests that it might be useful to point out the intuitive nature of the limit theorems in question.     

试论电子货币的界定

随着电子货币在经济活动中扮演着越来越重要的角色,人们对电子货币的研究也不断深入.但已有的研究都是基于多种不同的电子货币界定展开的,使得研究结论的可比性和一致性不高.本文参照传统货币的定义、职能等,扬弃现有研究对电子货币的界定,对电子货币给出明确界定,为进一步的研究打下基础.     

On certain compound frequency distributions

Abstract

Let ?(χ/y, z, …) be an ordinary frequency distribution where χ is the variate and y, z, … are parameters characterising the function. If then χ is a graduated variate fd 32_1 represents the probability of an observation drawn from this universe, falling between χ and χ + dχ. This probability is a function of χ. It is, however, also a function of the parameters. If one or more parameters are changed, this probability also changes. d f is a relative probability dependent on the values of y, z, …     

On equilibrium asset price processes

In this article we derive necessary and sufficient conditionsthat must be satisfied by equilibrium asset price processesin a pure exchange economy. We examine a world in which assetprices follow a diffusion process, asset markets are dynamicallycomplete, all investors maximize their (state-independent) expectedutility of consumption at some future date, and investors havenonrandom exogenous income. We show that it is necessary andsufficient that the coefficients of an equilibrium diffusionprice process satisfy a partial differential equation and aboundary condition. We also examine how the dynamics of assetprices are related to the shape of the representative investor'sutility function through the boundary condition. For example,in a constant-volatility economy, the expected instantaneousreturn of the market portfolio is mean reverting if and onlyif the relative risk aversion of the representative investoris decreasing in terminal wealth.     

A fitting procedure for some generalized poisson distributions

Abstract

Many of the contagious distributions considered in the biological sciences are members of the generalized Poisson family. Four distributions which belong to this family and have been used frequently are the Negative Binomial (cf. Bliss [2]), Neyman Type A (cf. Beall and Rescia [1]), Poisson Binomial (cf. McGuire et al. [10]) and the generalized Polya-Aeppli (cf. Skellam [14]).     

On cox processes and credit risky securities

A framework is presented for modeling defaultable securities and credit derivatives which allows for dependence between market risk factors and credit risk. The framework reduces the technical issues of modeling credit risk to the same issues faced when modeling the ordinary term structure of interest rates. It is shown how to generalize a model of Jarrow, Lando and Turnbull (1997) to allow for stochastic transition intensities between rating categories and into default. This generalization can handle contracts with payments explicitly linked to ratings. It is also shown how to obtain a term structure model for all different rating categories simultaneously and how to obtain an affine-like structure. An implementation is given in a simple one factor model in which the affine structure gives closed form solutions.     

On stationary point processes and Markov chains

Abstract

Introductory. In the theory of random processes we may distinguish between ordinary processes and point processes. The former are concerned with a quantity, say x (t), which varies with time t, the latter with events, incidences, which may be represented as points along the time axis. For both categories, the stationary process is of great importance, i. e., the special case in which the probability structure is independent of absolute time. Several examples of stationary processes of the ordinary type have been examined in detail (see e. g. H. Wold 1). The literature on stationary point processes, on the other hand, has exclusively been concerned with the two simplest cases, viz. the Poisson process and the slightly more general process arising in renewal theory (see e. g. J. Doob 3).     

First passage time for compound Poisson processes with diffusion: ruin theoretical and financial applications

In this paper, we propose to revisit Kendall’s identity (see, e.g. Kendall (1957)) related to the distribution of the first passage time for spectrally negative Lévy processes. We provide an alternative proof to Kendall’s identity for a given class of spectrally negative Lévy processes, namely compound Poisson processes with diffusion, through the application of Lagrange’s expansion theorem. This alternative proof naturally leads to an extension of this well-known identity by further examining the distribution of the number of jumps before the first passage time. In the process, we generalize some results of Gerber (1990 Gerber, H. U. (1990). When does the surplus reach a given target? Insurance: Mathematics and Economics 9, 115–119.  [Google Scholar]) to the class of compound Poisson processes perturbed by diffusion. We show that this main result is particularly relevant to further our understanding of some problems of interest in actuarial science. Among others, we propose to examine the finite-time ruin probability of a dual Poisson risk model with diffusion or equally the distribution of a busy period in a specific fluid flow model. In a second example, we make use of this result to price barrier options issued on an insurer’s stock price.     

论国有商业银行行长任期经济责任审计中的责任界定问题

经济责任界定是经济责任审计的重要内容.行长任期经济责任界定是否恰当准确、客观与否,关系到行长经济责任审计的质量,也关系到审计的风险,更关系到党和政府对干部使用的导向.本文结合学习贯彻中共中央办公厅、国务院办公厅印发<党政主要领导干部和国有企业领导人员经济责任审计规定>(以下简称<规定>)的体会,从实践出发,针对当前国有...     

论整肃行风行纪与加强农业银行内控建设

行风行纪作为一种特定的银行企业文化现象 ,构成银行内控环境的人文内容之一。行风行纪问题的主体是人 ,表征为文化 ,根子在制度。整肃行风行纪宜从大处着眼 ,即从制度创新、员工教育、监督制约三方面入手 ,构筑使人“不能做”、“不想做”、“不敢做”的内控环境。以期标本兼治。     

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.     

A computational definition of financial randomness

The aim of this study is to present an efficient and easy framework for the application of the Least Squares Monte Carlo methodology to the pricing of gas or power facilities as detailed in Boogert and de Jong [J. Derivatives, 2008, 15, 81–91]. As mentioned in the seminal paper by Longstaff and Schwartz [Rev. Financ. Stud. 2001, 113–147], the convergence of the Least Squares Monte Carlo algorithm depends on the convergence of the optimization combined with the convergence of the pure Monte Carlo method. In the context of the energy facilities, the optimization is more complex and its convergence is of fundamental importance in particular for the computation of sensitivities and optimal dispatched quantities. To our knowledge, an extensive study of the convergence, and hence of the reliability of the algorithm, has not been performed yet, in our opinion this is because the apparent infeasibility and complexity uses a very high number of simulations. We present then an easy way to simulate random trajectories by means of diffusion bridges in contrast to Dutt and Welke [J. Derivatives, 2008, 15 (4), 29–47] that considers time-reversal Itô diffusions and subordinated processes. In particular, we show that in the case of Cox-Ingersoll-Ross and Heston models, the bridge approach has the advantage to produce exact simulations even for non-Gaussian processes, in contrast to the time-reversal approach. Our methodology permits performing a backward dynamic programming strategy based on a huge number of simulations without storing the whole simulated trajectory. Generally, in the valuation of energy facilities, one is also interested in the forward recursion. We then design backward and forward recursion algorithms such that one can produce the same random trajectories by the use of multiple independent random streams without storing data at intermediate time steps. Finally, we show the advantages of our methodology for the valuation of virtual hydro power plants and gas storages.     

On the first passage time processes of brownian motion with positive drift

Abstract

The first passage time processes of Brownian Motion with positive drift are of considerable importance, particularly in life-testing or life-time situation as a natural consequence. It has been used in sequential analysis, e.g. finding the best test for testing the hypothesis of no drift versus the alternative of positive drift in a Brownian Motion. Various properties of the first passage time process of Brownian Motion with positive drift are reviewed and several new properties are investigated. In short, γ-variation properties, characterization, and behaviour at infinity are discussed.     

内部控制范畴定义探索

内部控制至今缺少范畴意义上的概念定义,导致理论研究难以深入。目前有关内部控制各方面研究,均因缺乏对内部控制基本属性特征、功能定位的确定认知,形成了一些难以判断理论贡献的虚假争论,从而带来了内部控制实践的盲目和不规范。在全球普遍高度关注内部控制问题的21世纪,加强对内部控制的理论研究成了时代呼声,而对内部控制范畴做出科学定义实属内部控制深化研究之瓶颈。文章根据逻辑学原理,综合运用人类学、生物学、社会学、组织学、管理学、经济学知识,认为"内部控制是运用专门手段工具及方法,防范与遏制非我与损我,保护与促进自我与益我的系统化制度";并以信息化为背景,对内部控制做出了便于计算机软件固化和动态优化运行的操作性框架定义。     

The valuation of compound options

This paper presents a theory for pricing options on options, or compound options. The method can be generalized to value many corporate liabilities. The compound call option formula derived herein considers a call option on stock which is itself an option on the assets of the firm. This perspective incorporates leverage effects into option pricing and consequently the variance of the rate of return on the stock is not constant as Black-Scholes assumed, but is instead a function of the level of the stock price. The Black-Scholes formula is shown to be a special case of the compound option formula. This new model for puts and calls corrects some important biases of the Black-Scholes model.     

On the discounted aggregate claim costs until ruin in dependent Sparre Andersen risk processes

In this paper, a dependent Sparre Andersen risk process in which the joint density of the interclaim time and the resulting claim severity satisfies the factorization as in Willmot and Woo is considered. We study a generalization of the Gerber–Shiu function (i) whose penalty function further depends on the surplus level immediately after the second last claim before ruin; and (ii) which involves the moments of the discounted aggregate claim costs until ruin. The generalized discounted density with a moment-based component proposed in Cheung plays a key role in deriving recursive defective renewal equations. We pay special attention to the case where the marginal distribution of the interclaim times is Coxian, and the required components in the recursion are obtained. A reverse type of dependency structure, where the claim severities follow a combination of exponentials, is also briefly discussed, and this leads to a nice explicit expression for the expected discounted aggregate claims until ruin. Our results are applied to generate some numerical examples involving (i) the covariance of the time of ruin and the discounted aggregate claims until ruin; and (ii) the expectation, variance and third central moment of the discounted aggregate claims until ruin.