Nonasymptotic analysis of robust regression with modified Huber's loss

To achieve robustness against the outliers or heavy-tailed sampling distribution, we consider an Ivanov regularized empirical risk minimization scheme associated with a modified Huber's loss for nonparametric regression in reproducing kernel Hilbert space. By tuning the scaling and regularization parameters in accordance with the sample size, we develop nonasymptotic concentration results for such an adaptive estimator. Specifically, we establish the best convergence rates for prediction error when the conditional distribution satisfies a weak moment condition.     

On some measures and distances for positive random variables

A number of conventional measures of risk as real‐valued functions on the space of positive random variables are considered: the expected shortfall, the mean excess over the threshold, the stop‐loss and some others. Ordering of risks, based on these measures and the distances between corresponding distribution functions, are described. The perturbed measures, describing the effect of changing environment, are discussed. These measures are defined by the accelerated life and proportional hazards models widely used in reliability and survival analysis. The case of a random environment is of a prime interest in the paper. The main result states that if, for instance, the stochastic environment is ‘neutral in expectation’ with respect to the baseline one, the distance between the corresponding distribution functions can be still sufficiently large. Copyright © 2003 John Wiley & Sons, Ltd.     

On the worst conditional expectation

We study continuous coherent risk measures on L^p, in particular, the worst conditional expectations. We show some representation theorems for them, extending the results of Artzner, Delbaen, Eber, Heath, and Kusuoka.     

股市风险构成间接分解模型的改进及实证

对Campbell等提出的分析股市风险构成的间接分解模型进行改进,并运用改进模型研究中国股票市场1995年至2005年的风险构成和趋势。结果发现,公司风险是个股收益率平均风险的最大组成部分,其次是系统风险,行业风险的重要性相对较小;中国股市收益率的平均风险随时间存在下降的趋势,而公司风险和行业风险的重要性随时间在增加;总的协方差风险序列对个股收益率平均风险的影响,随时间不具有一致性。在分析股市风险构成时,不应忽略对协方差风险序列的研究。     

Wireless network capacity management: A real options approach

This paper applies financial option valuation methods to new wireless network capacity investment decision timing. In particular, we consider the case of network capacity for cellular telephone service. Given a cluster of base stations (with a certain traffic capacity per base station), we determine when it is optimal to increase capacity for each of the base stations contained in the cluster. We express this in terms of the fraction of total cluster capacity in use, i.e. we calculate the optimal time to upgrade in terms of the ratio of observed usage to existing capacity. We study the optimal decision problem of adding new capacity in the presence of stochastic wireless demand for services. A four factor algorithm is developed, based on a real options formulation. Numerical examples are provided to illustrate various aspects of the model.     

Modelling of insurers’ rating determinants. An application of machine learning techniques and statistical models

In recent years, financial regulations such as Basel II and Solvency II have highlighted the utility of credit risk assessments through internal rating systems, particularly for estimating the probability of default (PD) of credit exposures.     

Structural models in consumer credit

We propose a structural credit risk model for consumer lending using option theory and the concept of the value of the consumer’s reputation. Using Brazilian empirical data and a credit bureau score as proxy for creditworthiness we compare a number of alternative models before suggesting one that leads to a simple analytical solution for the probability of default. We apply the proposed model to portfolios of consumer loans introducing a factor to account for the mean influence of systemic economic factors on individuals. This results in a hybrid structural-reduced-form model. And comparisons are made with the Basel II approach. Our conclusions partially support that approach for modelling the credit risk of portfolios of retail credit.     

一类随机保费率下的风险模型

引入随机变量保费率,对古典风险模型进行推广,主要研究随机保费率下的风险模型,用随机过程和鞅论的方法得出破产概率、末离前最大盈余分布、破产前瞬时盈余与破产赤字的联合分布等精算量分布的具体表达式.     

集合风险模型的可分解性

本文讨论了集合风险模型中 ,在复合二项分布和复合负二项分布两种情况下的可分解性问题 ,得到了同复合泊松分布情况下类似的结果     

Statistical approximations for recourse constrained stochastic programs

The two stage stochastic program with recourse is known to have numerous applications in financial planning, energy modeling, telecommunications systems etc. Notwithstanding its applicability, the two stage stochastic program is limited in its ability to incorporate a decision maker's attitudes towards risk. In this paper we present an extension via the inclusion of a recourse constraint. This results in a convex integrated chance constraint (ICC), which inherits the convexity properties of two stage programs. However, it also inherits some of the difficulties associated with the evaluation of recourse functions. This motivates our study of conditions that may be applicable to algorithms using statistical approximations of such ICC. We present a set of sufficient conditions that these approximations may satisfy in order to assure convergence. Our conditions are satisfied by a wide range of statistical approximations, and we demonstrate that these approximations can be generated within standard algorithmic procedures.This work was supported in part by Grant No. NSF-DDM-9114352 from the National Science Foundation.