Compound Poisson Model with Covariates

Abstract

Pet insurance in North America continues to be a growing industry. Unlike in Europe, where some countries have as much as 50% of the pet population insured, very few pets in North America are insured. Pricing practices in the past have relied on market share objectives more so than on actual experience. Pricing still continues to be performed on this basis with little consideration for actuarial principles and techniques. Developments of mortality and morbidity models to be used in the pricing model and new product development are essential for pet insurance. This paper examines insurance claims as experienced in the Canadian market. The time-to-event data are investigated using the Cox’s proportional hazards model. The claim number follows a nonhomogenous Poisson process with covariates. The claim size random variable is assumed to follow a lognormal distribution. These two models work well for aggregate claims with covariates. The first three central moments of the aggregate claims for one insured animal, as well as for a block of insured animals, are derived. We illustrate the models using data collected over an eight-year period.     

Portfolio selection with qualitative input

We formulate a mean-variance portfolio selection problem that accommodates qualitative input about expected returns and provide an algorithm that solves the problem. This model and algorithm can be used, for example, when a portfolio manager determines that one industry will benefit more from a regulatory change than another but is unable to quantify the degree of difference. Qualitative views are expressed in terms of linear inequalities among expected returns. Our formulation builds on the Black-Litterman model for portfolio selection. The algorithm makes use of an adaptation of the hit-and-run method for Markov chain Monte Carlo simulation. We also present computational results that illustrate advantages of our approach over alternative heuristic methods for incorporating qualitative input.     

投保过程为Poisson过程的一类保险精算模型研究

在传统保险产品定价方法研究基础上,以随机利率为研究前提,对保险公司在一段时间内的投保过程服从Poisson过程的保费收支情况进行了分析,分别讨论了保险公司收入和支出的精算现值,得到保险公司在一段时间内的保费计算模型。     

On Mixed and Compound Mixed Poisson Distributions

Recursive formulae are derived for the evaluation of the t-th order cumulative distribution function and the t-th order tail probability of 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. Also, some general results are derived for the evaluation of the t-th order moments of stop-loss transforms. The recursions can be applied for the exact evaluation of the probability function, distribution function, tail probability and stop-loss premium of compound mixed Poisson distributions and the corresponding mixed Poisson distributions. Several examples are also presented.     

Tobin tax and market depth

This paper investigates—on the basis of the Cont–Bouchaud model—whether a Tobin tax can stabilize foreign exchange markets. Compared to earlier multi-agent studies, this paper explicitly recognizes that a transaction tax-induced reduction in market depth may increase the price responsiveness of a given order. We find that the imposition of a transaction tax may still achieve a triple dividend: (1) exchange rate fluctuations decrease, (2) currencies are less mispriced and (3) central authorities raise substantial tax revenues. However, if the price impact function is too sensitive with respect to market depth, stabilization may turn into destabilization.     

On Ponzi schemes in infinite horizon collateralized economies with default penalties

We show, by means of an example, that in models where default is subject to both collateral repossession and utility punishments, opportunities for doing Ponzi schemes are not always ruled out and (refined) equilibria may fail to exist. This is true even if default penalties are moderate as defined in Páscoa and Seghir (Game Econ Behav 65:270–286, 2009). In our example, asset promises and default penalties are chosen such that, if an equilibrium does exist, agents never default on their promises. At the same time collateral bundles and utility functions are such that the full repayment of debts implies that the asset price should be strictly larger than the cost of collateral requirements. This is sufficient to induce agents to run Ponzi schemes and destroy equilibrium existence.     

Share Valuation under Geometric Brownian Motion with a Poisson Imputation Tax Change

A share valuation model is developed on the basis of dividends following a geometric Brownian motion. An imputation tax system is chosen, although this can be collapsed into a classical system. The possibility of changes in tax rates and shareholder tax credits is introduced by means of a Poisson jump. Capital gains are assumed to be tax-free through either annual or other exemptions. Using Itô's Lemma, a new share valuation formula is derived. This is recast in terms of the cost of capital and the mean time to the fiscal shock.     

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.     

Analysis of ruin measures for the classical compound Poisson risk model with dependence

In this paper, we consider an extension to the classical compound Poisson risk model. Historically, it has been assumed that the claim amounts and claim inter-arrival times are independent. In this contribution, a dependence structure between the claim amount and the interclaim time is introduced through a Farlie–Gumbel–Morgenstern copula. In this framework, we derive the integro-differential equation and the Laplace transform (LT) of the Gerber–Shiu discounted penalty function. An explicit expression for the LT of the discounted value of a general function of the deficit at ruin is obtained for claim amounts having an exponential distribution.     

The multinomial option pricing model and its Brownian and Poisson limits

The Cox, Ross, and Rubinstein binomial model is generalizedto the multinomial case. Limits are investigated and shown toyield the Black-Scholes formula in the case of continuous samplepaths for a wide variety of complete market structures. In thediscontinuous case of Merton-type formula is shown to result,provided jump probabilities are replaced by their correspondingArrow-Debreu prices.     

Scale economies and input price elasticities in microfinance institutions

We evaluate the efficiency of microfinance institutions (MFIs) using a structural approach which also captures these institutions’ outreach and sustainability objectives. We estimate economies of scale and input price elasticities for lending-only and deposit-mobilizing MFIs using a large sample of high-quality panel data. The results confirm conjectures that improvements in efficiency can come from the growth or consolidations of MFIs, as we find substantial increasing returns to scale for all but profitability-focused deposit-mobilizing MFIs. Our results support the existence of a trade-off between outreach and sustainability. All inputs are inelastic substitutes, but we find differences in own-price elasticities in lending-only and deposit-mobilizing MFIs.     

不断拓宽资本市场的广度和深度

在中国资本市场逐渐回暖、投资者信心逐渐恢复的背景下，中国应该借此机会，不断拓宽资本市场的广度和深度，从而为资本市场的持续健康发展奠定基础。     

机房端到端双电源交流输入的设计

机房设备的逐渐增多和单位面积功率的逐渐增大,对交流供电系统的可靠性和安全性提出了更高的要求,需要交流UPS系统能够提供安全、稳定、可靠、全天候无中断、优质的电源服务。目前多数金融机构的机房UPS都由原来的双机冗余并联系统升级到UPS双母线工作方式,并在UPS输入端采用了双电源自动切换（ATS）来实现UPS输入端的可靠性。     

城乡统筹发展的理论梳理和深入探讨

无论是马克思主义还是西方新古典主义或者发展经济学都从不同层面上深入探讨了城乡统筹的本质和关键内容。统筹城乡经济社会发展必须深入研究造成中国二元经济结构的一般和特殊性问题。总结中国城乡发展失衡的内在机理,除了中国特色的工业化道路诱致和加剧了城乡二元结构的产生,一系列配套政策的实施则固化了二元结构的现状。中国二元经济结构的转变,不仅要实现农业剩余劳动力的转移,而且必须全面解决“三农”问题以及城市与乡村、经济和社会的协调发展问题。     

Beyond the mundane: reconciling breadth and depth in futures enquiry

For some time there has been a need within Futures Studies (FS) to develop methods which go beyond the dominant empirical tradition. For many years there has been a near-exclusive emphasis on understanding the external world ‘out there’. But as time has gone by, so it has become clear that our ability to understand the world ‘out there’ crucially depends on an underlying world of reference that is ‘in here’. Understanding the near-future environment calls for a combination of ‘inner’ and ‘outer’ views which, for example, give as much credence to judgment as to calculation. This paper considers a way of considering these very different ‘ways of knowing’. Overall, the aim is to go beyond what might be termed ‘mundane’ analysis, i.e. that which is preoccupied with surfaces, and to open out a broader arena for futures enquiry.     

International P/L insurance output,input, and productivity comparisons

This research provides (bilateral) divisia and multilateral divisia indexes of output, input, and productivity for the property-liability (P-L) insurance industry for the following countries: United States, West Germany, Switzerland, France, and Japan. The time period studied is 1975 to 1987. The results indicate that considerable diversity exists among different countries, with Japan showing the weakest productivity growth. The United States and West Germany are associated overall with high productivity.     

PKI数据存储及发布

一、PKI概念数字证书是可以提供网络上身份证明的一种数字标识,包含特定对象的公开密钥。数字证书的拥有者可以将其证书提供给其他人、Web站点及网络资源,以证实其合法身份,并可与对方建立加密的、可信的通信。比如,用户可以使用证书通过浏览器与Web服务器建立SSL会话,使浏览器     

奏响三部曲 履职结硕果——记人民银行唐山市中心支行党委书记、行长陈志强

2010年5月,陈志强同志就任人民银行唐山中心支行党委书记、行长以来,团结带领全行干部职工,紧紧围绕履职提效这一工作中心,因地制宜、敢为人先,奏响"货币政策、金融稳定、金融服务"三部曲,开创性地履行了基层央行职责。近三年来,先后获得全国文明单位、全国总工会"模范职工小家"、中国人民银行文明单位等集体先进荣誉称号74项,在天津分行业绩考核中连续七年获得A级第一名。