学习理论中回归问题的误差估计(英文)

本文在一般的损失函数ψ(y-f(x))下,当ψ(z)连续时,讨论了学习理论中回归问题的误差估计.     

基于Copula-EVT模型的我国股票市场流动性调整的VaR和ES研究

结合相依结构函数Copula和极值理论EVT,构建了我国股票市场经流动性调整的La-Copula-EVT风险价值模型,并用沪深收益序列的分笔高频数据进行了实证分析,发现我国沪深股市收益序列的上尾和下尾都存在较高相关性,后验测试结果表明构建的模型能够对实际损失进行很好的拟合;然后在该模型的基础上进一步分析了我国沪深股市的风险价值和预期不足在不同置信区间的敏感度差异,确定了适合La-Copula-EVT模型的最优置信度区间。     

基于回购契约的风险厌恶零售商的供应链协调

研究了由风险中性的供应商和风险厌恶的零售商组成的二级供应链协调问题.零售商的风险厌恶由CVaR来度量,研究表明：零售商的风险厌恶加剧了双重边际效应,恶化了供应链效益.为了实现供应链的协调,供应商提出回购契约以减轻零售商的风险顾虑引导其增加订货量,结果表明：当零售商的风险厌恶超过了一定的程度,回购契约不能实现供应链协调;当供应链可以通过回购契约实现协调时,供应链的协调利益可以在供应商和零售商之间进行任意的分配,具体的分配结果取决于他们的讨价还价能力.     

Exchangeable claim sizes in a compound Poisson‐type process

When dealing with risk models the typical assumption of independence among claim size distributions is not always satisfied. Here we consider the case when the claim sizes are exchangeable and study the implications when constructing aggregated claims through compound Poisson‐type processes. In particular, exchangeability is achieved through conditional independence, using parametric and nonparametric measures for the conditioning distribution. Bayes' theorem is employed to ensure an arbitrary but fixed marginal distribution for the claim sizes. A full Bayesian analysis of the proposed model is illustrated with a panel‐type data set coming from a Medical Expenditure Panel Survey (MEPS). Copyright © 2009 John Wiley & Sons, Ltd.     

Optimal risk transfer for agents with germs

We introduce a new class of risk measures called generalized entropic risk measures (GERMS) that allow economic agents to have different attitudes towards different sources of risk. We formulate the problem of optimal risk transfer in terms of these risk measures and characterize the optimal transfer contract. The optimal contract involves what we call intertemporal source-dependent quotient sharing, where agents linearly share changes in the aggregate risk reserve that occur in response to shocks to the system over time, with scaling coefficients that depend on the attitudes of each agent towards the source of risk causing the shock. Generalized entropic risk measures are not dilations of a common base risk measure, so our results extend the class of risk measures for which explicit characterizations of the optimal transfer contract can be found.     

Securitizing and tranching longevity exposures

We consider the problem of optimally designing longevity risk transfers under asymmetric information. We focus on holders of longevity exposures that have superior knowledge of the underlying demographic risks, but are willing to take them off their balance sheets because of capital requirements. In equilibrium, they transfer longevity risk to uninformed agents at a cost, where the cost is represented by retention of part of the exposure and/or by a risk premium. We use a signalling model to quantify the effects of asymmetric information and emphasize how they compound with parameter uncertainty. We show how the cost of private information can be minimized by suitably tranching securitized cashflows, or, equivalently, by securitizing the exposure in exchange for an option on mortality rates. We also investigate the benefits of pooling several longevity exposures and the impact on tranching levels.     

Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models

This research proposes a mortality model with an age shift to project future mortality using principal component analysis (PCA). Comparisons of the proposed PCA model with the well-known models—the Lee-Carter model, the age-period-cohort model (Renshaw and Haberman, 2006), and the Cairns, Blake, and Dowd model—employ empirical studies of mortality data from six countries, two each from Asia, Europe, and North America. The mortality data come from the human mortality database and span the period 1970-2005. The proposed PCA model produces smaller prediction errors for almost all illustrated countries in its mean absolute percentage error. To demonstrate longevity risk in annuity pricing, we use the proposed PCA model to project future mortality rates and analyze the underestimated ratio of annuity price for whole life annuity and deferred whole life annuity product respectively. The effect of model risk on annuity pricing is also investigated by comparing the results from the proposed PCA model with those from the LC model. The findings can benefit actuaries in their efforts to deal with longevity risk in pricing and valuation.     

On the optimal product mix in life insurance companies using conditional value at risk

This paper proposes a Conditional Value-at-Risk Minimization (CVaRM) approach to optimize an insurer’s product mix. By incorporating the natural hedging strategy of Cox and Lin (2007) and the two-factor stochastic mortality model of Cairns et al. (2006b), we calculate an optimize product mix for insurance companies to hedge against the systematic mortality risk under parameter uncertainty. To reflect the importance of required profit, we further integrate the premium loading of systematic risk. We compare the hedging results to those using the duration match method of Wang et al. (forthcoming), and show that the proposed CVaRM approach has a narrower quantile of loss distribution after hedging—thereby effectively reducing systematic mortality risk for life insurance companies.     

DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.     

Measuring the default risk of sovereign debt from the perspective of network

Recently, there has been a growing interest in network research, especially in the fields of biology, computer science, and sociology. It is natural to address complex financial issues such as the European sovereign debt crisis from the perspective of network. In this article, we construct a network model according to the debt–credit relations instead of using the conventional methodology to measure the default risk. Based on the model, a risk index is examined using the quarterly report of consolidated foreign claims from the Bank for International Settlements (BIS) and debt/GDP ratios among these reporting countries. The empirical results show that this index can help the regulators and practitioners not only to determine the status of interconnectivity but also to point out the degree of the sovereign debt default risk. Our approach sheds new light on the investigation of quantifying the systemic risk.