Moments of Compound Mixed Poisson Distributions

Recursive formulae are derived for the evaluation of the moments and the descending factorial moments about a point n of mixed Poisson and 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. As byproduct, we also obtain recursive formulae for the evaluation of the moments about the origin, central moments, descending and ascending factorial moments of these distributions. Examples are also presented for a number of mixing densities.     

Recursive Moments of Compound Renewal Sums with Discounted Claims

Under regularity conditions, Le´veille´& Garrido [6] gives a derivation of the first two moments (resp. asymptotic) of a Compound Renewal Present Value Risk (CRPVR) process using renewal theory arguments. In this paper, with the same procedure and assuming that all the moments of the claim severity and the claims number process exist, we get recursive formulas for all the moments (resp. asymptotic) of the CRPVR process.     

Martingale Approach for Moments of Discounted Aggregate Claims

We examine the Laplace transform of the distribution of the shot noise process using the martingale. Applying the piecewise deterministic Markov processes theory and using the relationship between the shot noise process and the accumulated/discounted aggregate claims process, the Laplace transform of the distribution of the accumulated aggregate claims is obtained. Assuming that the claim arrival process follows the Poisson process and claim sizes are assumed to be exponential and mixture of exponential, we derive the explicit expressions of the actuarial net premiums and variances of the discounted aggregate claims, which are the annuities paid continuously. Numerical examples are also provided based on them.     

On the Gerber-Shiu Discounted Penalty Function for the Ordinary Renewal Risk Model with Constant Interest

Abstract

In this paper we study the Gerber-Shiu discounted penalty function for the ordinary renewal risk model modified by the constant interest on the surplus. Explicit answers are expressed by an infinite series, and a relational formula for some important joint density functions is derived. Applications of the results to the compound Poisson model are given. Finally, a lower bound and an upper bound for the ultimate ruin probability are derived.     

Valuation and Cost of Capital Formulae with Corporate and Personal Taxes: A Synthesis Using the Dempsey Discounted Dividends Model

This paper advances expressions for the firm's valuation and cost of capital as a function of leverage. The framework is arrived at by introducing leverage in Dempsey's (1996 and 1998) cost of capital framework and is applicable in the context of both classical and imputation tax systems. The framework reveals that both the historical stability of corporate leverage and the firm's choice of financing structure as revealed by the Pecking Order hypothesis are consistent with a tax-based explanation.     

The Impact of Personal Taxes on the Firm's Weighted Average Cost of Capital and Investment Behaviour: A Simplified Approach Using the Dempsey Discounted Dividends Model

The discounted dividends model advanced by Dempsey (1996) is extended to provide a weighted average cost of capital (WACC) assessment of investment opportunities with irregular cash flows. Thereafter, the framework is extended to an assessment of the implications of government tax policy for the firm's investment behaviour. The developed framework is consistent with the empirical evidence of Poterba and Summers (1985) which — over the period of UK tax history 1950–1983 encompassing four major tax on equity reforms — observes how the related dividend and investment politics of UK firms appear to be influenced by the level of dividend taxes.     

The Expected Discounted Penalty at Ruin for a Markov-Modulated Risk Process Perturbed by Diffusion

Abstract

A Markov-modulated risk process perturbed by diffusion is considered in this paper. In the model the frequencies and distributions of the claims and the variances of the Wiener process are influenced by an external Markovian environment process with a finite number of states. This model is motivated by the flexibility in modeling the claim arrival process, allowing that periods with very frequent arrivals and ones with very few arrivals may alternate. Given the initial surplus and the initial environment state, systems of integro-differential equations for the expected discounted penalty functions at ruin caused by a claim and oscillation are established, respectively; a generalized Lundberg’s equation is also obtained. In the two-state model, the expected discounted penalty functions at ruin due to a claim and oscillation are derived when both claim amount distributions are from the rational family. As an illustration, the explicit results are obtained for the ruin probability when claim sizes are exponentially distributed. A numerical example also is given for the case that two classes of claims are Erlang(2) distributed and of a mixture of two exponentials.     

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。     

The Moments of the Time of Ruin in Markovian Risk Models

Abstract

We present an approach based on matrix-analytic methods to find moments of the time of ruin in Markovian risk models. The approach is applicable when claims occur according to a Markovian arrival process (MAP) and claim sizes are phase distributed with parameters that depend on the state of the MAP. The method involves the construction of a sample-path-equivalent Markov-modulated fluid flow for the risk model. We develop an algorithm for moments of the time of ruin and prove the algorithm is convergent. Examples show that the proposed approach is computationally stable.     

货币周期视角下债券市场信用风险门槛效应及调控策略选择

在当前经济结构调整与货币周期宽紧转换的宏观背景下,市场利率对债券市场信用风险的影响可能具有门槛效应。通过对货币周期转换阶段市场利率对债券市场信用风险的影响机制进行分析,以2012年1月—2017年8月我国宏观数据为样本,建立门槛模型来捕捉市场利率对债券市场信用风险的非线性影响特征。实证结果表明,不同期限结构的市场利率变化对债券市场信用风险影响效果存在显著差异,长期利率整体上对信用风险具有正向影响,短期利率则视货币宽紧程度对信用风险有截然相反的影响效果。进而提出中央银行可根据货币周期所处不同阶段在公开市场上采取不同的操作策略组合,综合运用多种政策工具调节不同期限结构的市场目标利率,以优化货币政策和宏观审慎政策相结合的金融调控能力,防范债券市场信用风险,促进金融市场稳健发展。     

Background Risk in the Principal-Agent Model

We examine the effect of background risk in the standard two-state, two-action principal-agent model. We analyse situations where the background risk is environmental (always present) and where the background risk is contractual (only present if the contract is accepted). With contractual background risk, expected wages always rise and the incentive scheme is flatter if the agent's preferences satisfy weak decreasing absolute risk aversion. With environmental background risk, the optimal incentive scheme becomes flatter if the agent is weakly prudent. We provide conditions under which the environmental background risk decreases the agent's expected wage.     

Analysis of a Generalized Penalty Function in a Semi-Markovian Risk Model

Abstract

In this paper an extension of the semi-Markovian risk model studied by Albrecher and Boxma (2005) is considered by allowing for general interclaim times. In such a model, we follow the ideas of Cheung et al. (2010b) and consider a generalization of the Gerber-Shiu function by incorporating two more random variables in the traditional penalty function, namely, the minimum surplus level before ruin and the surplus level immediately after the second last claim prior to ruin. It is shown that the generalized Gerber-Shiu function satisfies a matrix defective renewal equation. Detailed examples are also considered when either the interclaim times or the claim sizes are exponentially distributed. Finally, we also consider the case where the claim arrival process follows a Markovian arrival process. Probabilistic arguments are used to derive the discounted joint distribution of four random variables of interest in this risk model by capitalizing on an existing connection with a particular fluid flow process.     

中国影子银行对银行风险承担阈值效应的实证研究

本文以影子银行对银行风险承担的双重作用为出发点,在理论证明影子银行对银行风险承担可能存在阈值效应的基础上,进一步构建动态非线性面板模型进行实证检验。结果表明:我国影子银行的发展与银行风险承担之间呈U形关系,存在阈值效应,阈值点出现在2013年左右;我国影子银行的发展对银行风险承担的影响程度依赖于银行资本情况、经营效率与资产规模;银行风险承担与内、外部影子银行规模之间均呈U形关系,但分别位于U形曲线的前半段与后半段,即目前内部影子银行发展有助于降低银行风险承担,而外部影子银行发展则倾向于提高银行风险承担。     

物联网技术背景下商业银行操作风险研究——基于超越阈值模型

物联网技术的迅速发展,为我国商业银行操作风险管理带来了新的思路,根据巴塞尔委员会对操作风险的分类,结合物联网技术在银行的应用,将操作风险划分为五个类别:内部欺诈风险、外部欺诈风险、质押物丢失损坏风险、从业人员操作失误风险、物联网系统风险。通过收集我国商业银行20102017年间的各类型操作风险的损失数据,构建POT超越阈值模型对操作风险进行实证分析,并对比了基于物联网技术的商业银行操作风险和传统商业银行操作风险的ES值,结果表明前者可以有效降低操作风险,因此商业银行应大力推行对物联网技术的部署及应用。最后,提出了基于物联网技术的商业银行操作风险管理建议。     

基于分层模型的银行客户信用风险预测研究

本文基于商业银行客户信贷记录数据集,通过运用拉普拉斯分层模型对客户的信用风险进行预测研究.利用客户群体存在差异化的特点,采用XGBoost机器学习算法来选择分层特征以及结合多元特征的组合形式来预测客户的违约情况.在不同分层特征结构下依次对比拉普拉斯分层模型、单独模型、共同模型和随机森林四个模型的预测效果,并建立模拟数据集来对拉普拉斯分层模型的性能进行验证.研究发现:(1)拉普拉斯分层模型的预测精度是最高的,预测性能具有稳定性;(2)本文数据集所适用的最佳分层特征是贷款金额、年龄和婚姻;(3)分层特征的选择和数量会依据不同数据而产生相应变化,并非一成不变.结合本文的研究思路和结果,以期为商业银行在客户信用风险评估实践中提供新的思考和建议.     

Bounds for Ratios of Posterior Expectations: Applications in the Collective Risk Model

This paper considers the collective risk model for the insurance claims process. We will adopt a Bayesian point of view, where uncertainty concerning the specification of the prior distribution is a common question. The robust Bayesian approach uses a class of prior distributions which model uncertainty about the prior, instead of a single distribution. Relatively little research has dealt with robustness with respect to ratios of posterior expectations as occurs with the Esscher and Variance premium principles. Appropriate techniques are developed in this paper to solve this problem using the k -contamination class in the collective risk model.     

治理结构在银行风险管理战略中的角色定位

现代商业银行越来越意识到风险管理的重要性,并将之放在一个战略的高度。本从组织回应战略的角度,研究公司治理在银行施行风险管理战略过程中所扮演的角色,探讨了中国银行业如何定位治理组织结构,以适应风险管理战略的需要。     

企业债务风险处置策略研究

本文总结近几年产能过剩行业企业债务风险的不同处置模式,分析了银行、政府、企业在企业债务风险爆发后的策略博弈行为,发现企业负债规模越大,负债结构越复杂,政府在企业重组(整)中应该发挥的主导作用就应该越强。管理者应该根据企业和市场状况及时选定合理的重组(整)模式,提高债务风险处置效率。     

收益现值法在发电企业整体资产评估中的应用

本文结合实践中的评估操作,对目前国内应用收益现值法评估发电企业中评估参数的确定、操作的注意事项以及存在的主要问题,提出了自己的观点.可选择的企业价值评估方法有资产基础法、收益现值法和市场法三种,其中收益现值法常常是企业整体资产评估必须选择的方法.但目前国内对于发电企业的整体价值评估,几乎千篇一律地采用成本加和法.即使有些评估机构和评估人员采用了收益现值法,也只是对成本加和法评估结果进行辅助性的验证.这种状况的形成既有历史原因,又有现阶段企业价值评估的客观条件的原因.总之,收益现值法在国内企业整体价值的评估中还没有得到普遍准确地应用.本文结合了近年的评估工作实践,讨论了收益现值法在国内发电企业的整体价值操作中存在的问题与处理方法.