Correspondence between lifetime minimum wealth and utility of consumption

We establish when the two problems of minimizing a function of lifetime minimum wealth and of maximizing utility of lifetime consumption result in the same optimal investment strategy on a given open interval O in wealth space. To answer this question, we equate the two investment strategies and show that if the individual consumes at the same rate in both problems—the consumption rate is a control in the problem of maximizing utility—then the investment strategies are equal only when the consumption function is linear in wealth on O, a rather surprising result. It then follows that the corresponding investment strategy is also linear in wealth and the implied utility function exhibits hyperbolic absolute risk aversion.      

Stochastic Orderings of Convex-Type for Discrete Bivariate Risks

New classes of order relations for discrete bivariate random vectors are introduced that essentially compare the expectations of real functions of convex-type of the random vectors. For the actuarial context, attention is focused on the so-called increasing convex orderings between discrete bivariate risks. First, various characterizations and properties of these orderings are derived. Then, they are used for comparing two similar portfolios with dependent risks and for constructing bounds on several multilife insurance premiums.     

论高等财经类院校《概率论》课程教学过程中数学思想的渗透

高等财经类院校《概率论》课程教学过程中需要注重数学思想的渗透,不仅要使学生掌握概率论的基础知识,更重要的是训练学生严密的科学思维及分析解决问题的能力,为学生学习后继课程打下良好的基础。     

La loi de Pareto et la réassurance

Abstract

Nous allons étudier l'influence de la distribution des sommes assurées sur Ie risque mathématique d'une compagnie. Qu'il soit permis de développer tout d'abord notre vue générule sur Ie probleme du risque.     

信用风险度量技术的最新发展及其在贷款定价中的运用

进入21世纪后,对产生于上个世纪的信用风险计量技术的持续研究进一步提高了风险计量的敏感度和准确度。本文剖析了主要的信用风险计量模型对风险变量的测算方法和适用性,探讨其最新发展,并分析了信用风险计量新技术在贷款定价的运用。     

信用风险限额的构建方法——内部评级体系的应用

本文结合银行授信业务和《巴塞尔新资本协议》的要求,从理论上解析了公司授信业务中的信用风险限额(Credit Limit)的结构、层次;并从实施角度提供了具体的计算办法。作者首次提出了条件违约概率的概念,并介绍如何应用条件违约概率构建风险限额。鉴于集团公司客户在管理中的重要性,作者重点讨论了集团公司限额制定的办法和规则,介绍了如何综合利用客户评级信息来计算信用风险限额。此外,本文围绕信用风险限额介绍了授信业务中的交易结构优化、客户评级系统相关的概念。     

On a risk model with dependence between interclaim arrivals and claim sizes

We consider an extension to the classical compound Poisson risk model for which the increments of the aggregate claim amount process are independent. In Albrecher and Teugels (2006 Albrecher, H. and Teugels, J. 2006. Exponential behavior in the presence of dependence in risk theory. Journal of Applied Probability, 43(1): 257–273. [Crossref], [Web of Science ®] , [Google Scholar]), an arbitrary dependence structure among the interclaim time and the subsequent claim size expressed through a copula is considered and they derived asymptotic results for both the finite and infinite-time ruin probabilities. In this paper, we consider a particular dependence structure among the interclaim time and the subsequent claim size and we derive the defective renewal equation satisfied by the expected discounted penalty function. Based on the compound geometric tail representation of the Laplace transform of the time to ruin, we also obtain an explicit expression for this Laplace transform for a large class of claim size distributions. The ruin probability being a special case of the Laplace transform of the time to ruin, explicit expressions are therefore obtained for this particular ruin related quantity. Finally, we measure the impact of the various dependence structures in the risk model on the ruin probability via the comparison of their Lundberg coefficients.     

Corporate governance and the probability of default

We employ Merton's probability of default as a continuous ex‐ante measure of the likelihood of firm failure and dynamic panel generalised method of moments to better characterise the relationship between corporate governance and the chance of default. In doing so, we overcome limitations of discrete proxies widely used in previous studies and more completely account for endogeneity issues permeating this area of research. While initial testing designed to facilitate comparison with previous studies suggests a significant relationship between the probability of default and executive pay, board structure and ownership structure, once endogeneity concerns are accounted for, no such relationship remains.     

Measurement of the Severity of Opportunistic Fraud in Injury Insurance: Evidence from China

This article assesses the effects of claimant demographics and other claim characteristics on the measurement of the severity of opportunistic fraud using 96 excess claim lawsuits in personal injury insurance in China in 2000–2012. The empirical result indicates that severe opportunistic fraud that results in death is more numerous than it is for fraud that leads to disability and nondisability, which may be due to the fact that more severe injury may create greater openings for opportunistic fraud. Second, the severity of opportunistic fraud in provincial cities is lower than that in small or midsize cities because the former does not imply greater severity of opportunistic fraud. Third, the severity of opportunistic fraud in injuries from daily activity is greater than that for injuries from work and traffic accidents, implying that a higher excess claim probability and greater severity of opportunistic fraud in injuries from daily activity are consistent.     

A generalised Gerber–Shiu measure for Markov-additive risk processes with phase-type claims and capital injections

In this paper we consider a risk reserve process where the arrivals (either claims or capital injections) occur according to a Markovian point process. Both claim and capital injection sizes are phase-type distributed and the model allows for possible correlations between these and the inter-claim times. The premium income is modelled by a Markov-modulated Brownian motion which may depend on the underlying phases of the point arrival process. For this risk reserve model we derive a generalised Gerber–Shiu measure that is the joint distribution of the time to ruin, the surplus immediately before ruin, the deficit at ruin, the minimal risk reserve before ruin, and the time until this minimum is attained. Numeral examples illustrate the influence of the parameters on selected marginal distributions.     

IRB法下公司敞口组合的风险驱动因子计量研究

巴塞尔银行监管委员会针对防范信贷组合信用风险所需要的资本制定的内部评级法,通过风险驱动因子的变化来反映组合回报的变化,并根据风险权重函数,通过风险加权资产转化为与每一项信用风险敞口更准确匹配的资本要求.本文对违约概率、违约损失率、违约敞口、期限因素以及违约相关性等信贷组合信用风险的风险驱动因子的度量进行了综合研究.