Some estimation problems connected with compound poisson processes

Abstract

The problems of this report have, for the particular case where the process considered in section 1 below reduces to a time- and spacehomogeneous Poisson process, been propounded by Gunnar Benktander who kindly gave his comments to the author.     

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 a symmetrization of diffusion processes

The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion processes. The present paper aims to give a basis to the use of the numerical scheme for Heston and SABR-type stochastic volatility models. This will be done by showing a fairly general result on the symmetrization (in multi-dimension/multi-reflections). Further applications (to time-inhomogeneous diffusions/ to time-dependent boundaries/to curved boundaries) are also discussed.     

On alternative interest rate processes

In this paper alternative interest rate processes are estimated for Denmark, Germany, Sweden, and the UK, using the generalized method of moments (GMM). In line with the study by Chan, Karolyi, Longstaff, and Sanders (1992) on US data, there seems to be a positive relation between interest rate level and volatility for some countries. In contrast to their study, it is found that mean-reversion plays an important role for the specification of the interest rate dynamics. The results seem to be robust to the use of different moment conditions, and simulations of the estimated models reveal that they are fairly able to capture non-fitted moments as well. In addition, there is evidence of a structural change in the Danish interest rate process in August 1985, which may be due to a change in monetary policy. The small sample properties of the GMM estimators are also studied through simulations.     

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 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).     

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.     

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.     

On a multi-threshold compound Poisson surplus process with interest

We consider a multi-threshold compound Poisson surplus process. When the initial surplus is between any two consecutive thresholds, the insurer has the option to choose the respective premium rate and interest rate. Also, the model allows for borrowing the current amount of deficit whenever the surplus falls below zero. Starting from the integro-differential equations satisfied by the Gerber–Shiu function that appear in Yang et al. (2008), we consider exponentially and phase-type(2) distributed claim sizes, in which cases we are able to transform the integro-differential equations into ordinary differential equations. As a result, we obtain explicit expressions for the Gerber–Shiu function.     

A Markov-switching generalized additive model for compound Poisson processes,with applications to operational loss models

This paper is concerned with modelling the behaviour of random sums over time. Such models are particularly useful to describe the dynamics of operational losses, and to correctly estimate tail-related risk indicators. However, time-varying dependence structures make it a difficult task. To tackle these issues, we formulate a new Markov-switching generalized additive compound process combining Poisson and generalized Pareto distributions. This flexible model takes into account two important features: on the one hand, we allow all parameters of the compound loss distribution to depend on economic covariates in a flexible way. On the other hand, we allow this dependence to vary over time, via a hidden state process. A simulation study indicates that, even in the case of a short time series, this model is easily and well estimated with a standard maximum likelihood procedure. Relying on this approach, we analyse a novel data-set of 819 losses resulting from frauds at the Italian bank UniCredit. We show that our model improves the estimation of the total loss distribution over time, compared to standard alternatives. In particular, this model provides estimations of the 99.9% quantile that are never exceeded by the historical total losses, a feature particularly desirable for banking regulators.     

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.     

On jump processes in the foreign exchange and stock markets

This article investigates the existence of discontinuities inthe sample path of exchange rates and of a stock market index.Maximum-likelihood estimation of a mixed jump-diffusion processreveals that exchange rates exhibit systematic discontuinities,even after allowing for conditional heteroskedasticity in thediffusion process. The results are much more significant inthe foreign exchange market than in the stock market, whichsuggests differences in the structure of these markets. Finally,this jump component is shown to explain some of the empiricallyobserved mispricings in the currency options market.