Economic Capital Allocation Derived from Risk Measures

Abstract

We examine properties of risk measures that can be considered to be in line with some “best practice” rules in insurance, based on solvency margins. We give ample motivation that all economic aspects related to an insurance portfolio should be considered in the definition of a risk measure. As a consequence, conditions arise for comparison as well as for addition of risk measures. We demonstrate that imposing properties that are generally valid for risk measures, in all possible dependency structures, based on the difference of the risk and the solvency margin, though providing opportunities to derive nice mathematical results, violates best practice rules. We show that so-called coherent risk measures lead to problems. In particular we consider an exponential risk measure related to a discrete ruin model, depending on the initial surplus, the desired ruin probability, and the risk distribution.     

Absolute Ruin Probabilities in a Jump Diffusion Risk Model with Investment

Abstract

This article considers the compound Poisson insurance risk model perturbed by diffusion with investment. We assume that the insurance company can invest its surplus in both a risky asset and the risk-free asset according to a fixed proportion. If the surplus is negative, a constant debit interest rate is applied. The absolute ruin probability function satisfies a certain integro-differential equation. In various special cases, closed-form solutions are obtained, and numerical illustrations are provided.     

Ruin Problems for Phase-Type(2) Risk Processes

In this paper we consider a risk process in which claim inter-arrival times have a phase-type(2) distribution, a distribution with a density satisfying a second order linear differential equation. We consider some ruin related problems. In particular, we consider the compound geometric representation of the infinite time survival probability, as well as the (defective) distributions of the surplus immediately prior to ruin and of the deficit at ruin. We also consider explicit solutions for the infinite time ruin probability in the case where the individual claim amount distribution is phase-type.     

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.     

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.     

On the Joint Distributions of the Time to Ruin,the Surplus Prior to Ruin,and the Deficit at Ruin in the Classical Risk Model

Abstract

The seminal paper by Gerber and Shiu (1998) unified and extended the study of the event of ruin and related quantities, including the time at which the event of ruin occurs, the deficit at the time of ruin, and the surplus immediately prior to ruin. The first two of these quantities are fundamentally important for risk management techniques that utilize the ideas of Value-at-Risk and Tail Value-at-Risk. As is well known, calculation of these and related quantities requires knowledge of the associated probability distributions. In this paper we derive an explicit expression for the joint (defective) distribution of the time to ruin, the surplus immediately prior to ruin, and the deficit at ruin in the classical compound Poisson risk model. As a by-product, we obtain expressions for the three bivariate distributions generated by the time to ruin, the surplus prior to ruin, and the deficit at ruin. Finally, we consider mixed Erlang claim sizes and show how the joint (defective) distribution of the time to ruin, the surplus prior to ruin, and the deficit at ruin can be calculated.     

基于信用风险管理视角的信用衍生产品创新

20世纪90年代以来,信用衍生品市场蓬勃发展,已经成为商业银行进行信用风险管理的重要手段,研究和引进这一新兴的金融工具,对于提高我国商业银行信用风险管理水平具有积极的意义。本文对银行业信用风险的产生和管理以及信用衍生产品作了介绍,对我国引进这一金融产品进行了分析并提出了建议。     

The Ruin Probability of a Discrete Time Risk Model under Constant Interest Rate with Heavy Tails

This paper investigates the ultimate ruin probability of a discrete time risk model with a positive constant interest rate. Under the assumption that the gross loss of the company within one year is subexponentially distributed, a simple asymptotic relation for the ruin probability is derived and compared to existing results.     

The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Abstract:  Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay-offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall-based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean-shortfall portfolios can be much greater than for mean-variance portfolios. Using empirical hedge fund return data we show that the optimal mean-shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short-put payoffs are optimal for a mean-shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.     

Detecting Linear and Nonlinear Dependence in Stock Returns: New Methods Derived from Chaos Theory

Interest in the relevance of nonlinear dynamics to fields such as finance and economics has spurred the development of new methods of analysis for time series data. Early tests for chaos led to problems when applied to financial and economic data. This motivated development of the BDS family of statistics to test for nonlinearity generally. More recently, another method of analysis has been introduced into the scientific literature. It uses a test for chaos which is relatively simple and appropriate for financial data. A quantitative version of this test is developed here and is used to analyze stock return data.     

贷款风险度量在农村信用社信贷管理中的应用

防范信贷风险是农村信用社风险管理的主要任务。贷款风险度量是贷款风险管理的重点和难点,对防范和控制贷款风险起着至关重要的作用。本文描述了贷款对象、形式、期限和形态对于贷款风险度影响的差异性及其风险权数的确定,重点探讨了贷款风险度量在农村信用社贷款决策审批、信贷检查、风险监测及控制管理方面的应用方法。     

社保基金境外投资风险及其防范

随着《全国社保基金境外投资管理暂行办法》的即将出台,社保基金将要进行海外投资。社保基金海外投资将遇到信息披露和交易成本问题、市场流动性风险、国家风险和税收等问题,为了防范风险必须要加强对社保基金境外投资的风险管理。     

我国证券公司风险测度指标体系的建立

随着我国加入WTD,国内资本市场必将加大对外开放力度,逐步与国际资本市场接轨.但由于许多主客观原因,国内证券公司在风险管理方面与西方金融机构相比还有相当大的差距,既有制度体系方面的不足,又有技术工具方面的缺乏.因此,如何提高我国证券公司风险测度水平是一个紧迫而又重要的课题.本文正是基于以上原因对我国证券公司风险测试从技术上进行了探讨.     

Direct Derivation of Finite-Time Ruin Probabilities in the Discrete Risk Model with Exponential or Geometric Claims

Abstract

Growing research interest has been shown in finite-time ruin probabilities for discrete risk processes, even though the literature is not as extensive as for continuous-time models. The general approach is through the so-called Gerber-Shiu discounted penalty function, obtained for large families of claim severities and discrete risk models. This paper proposes another approach to deriving recursive and explicit formulas for finite-time ruin probabilities with exponential or geometric claim severities. The proposed method, as compared to the general Gerber-Shiu approach, is able to provide simpler derivation and straightforward expressions for these two special families of claims.     

借鉴风险管理理论创新税收管理体制机制

我国税收管理体制机制存在的一些突出的矛盾和问题,制约着税收管理实现科学化、专业化、精细化,制约着税收征管质量和效率的有效提高.风险管理理论为有效解决上述矛盾和问题提供了重要启示和有效路径.借鉴风险管理理论,创新我国税收管理的体制机制,有利于实现税收管理效能的最大化,不断提高税收管理的水平和质量.     

经济开放中的中国金融风险报告和政策措施

经济开放中的中国金融安全问题,包括金融机构、金融市场、货币安全等等,成为中国各界关注的问题。本文旨在为经济开放中的中国金融业发展提供一个完整的风险报告,并在此基础上演绎出有关中国金融发展的建设性政策措施,由此消减所潜在的金融危机压力。     

对银行高管操作风险的经济学分析

本文通过构建“银行高管—银行监管人员”之间的跨时博弈模型,对当前银行面临的“由银行高管引发的操作风险问题”这一重要课题进行了理论上的探讨。基本结论如下:一、银行高管是否违规取决于其预期总收益和违规预期总成本的比较;而银行监管人员的查处力度大小则决定了其违规金额的大小。二、现实中,由银行高管引发的操作风险不可能被完全消除,监管机构和监管人员必须存在。三、银行高管和监管人员之间的博弈是否存在一个稳定均衡解,取决于他们各自效用函数的具体形式以及模型中各外生参数的取值,对这点的认识对政策的制定将有根本的导向作用。     

风险管理的理念与标准

养老基金在投资管理过程中面临各种各样的风险范畴。从外部看,包括法律和政治风险、利率变化风险、通货膨胀风险和市场波动风险等;从内部看,包括治理和道德风     

An Industrial Organization Theory of Risk Sharing

Examining the global reinsurance market, we propose a new theory of optimal risk sharing that finds its inspiration in the economic theory of the firm. Our model offers a theoretical foundation for two empirical regularities that are observed in the reinsurance market: (1) the choice of specific attachment (the deductible) and detachment points (the policy limits or the retrocession); and (2) the vertical and horizontal tranching of reinsurance contracts. Using a two-factor cost model, we show how reinsurance should be optimally layered (with attachment and detachment points) for a given book of business in order to minimize the cost and total premium associated with catastrophic events.