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FINITE-TIME RUIN PROBABILITY WITH NQD DOMINATED VARYING-tailED CLAIMS AND NLOD INTER-ARRIVAL TIMES

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Journal of Systems Science & Complexity 2009年第3期22卷 407-414页

作者： Jingzhi LI Kaiyong WANG Yuebao WANG Department of Mathematics Soochow University Suzhou 215006 China. Department of Mathematics Soochow University Suzhou 215006 China Department of Information and Com-putational Science School of Mathematics and Physics Suzhou University of Science and Technology Suzhou215009 China.

In 2007,Chen and Ng investigated infinite-time ruin probability with constant interest forceand negatively quadrant dependent and extended regularly varying-tailed *** this work,the authors obtain a weakly asymptotic equivalent formula for the finite-time and infinite-time ruinprobability with constant interest force,negatively quadrant dependent,and dominated varying-tailedclaims and negatively lower orthant dependent inter-arrival *** particular,when the claims areconsistently varying-tailed,an asymptotic equivalent formula is presented.

关键词： heavy tail negatively lower orthant dependent negatively quadrant dependent renewalmodel ruin probability.

Nearly optimal Bayesian shrinkage for high-dimensional regression

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Science China Mathematics 2023年第2期66卷 409-442页

作者： Qifan Song Faming Liang Department of Statistics Purdue UniversityWest LafayetteIN 47906USA

During the past decade,shrinkage priors have received much attention in Bayesian analysis of high-dimensional *** paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,which has a heavy and flat tail and allocates a sufficiently large probability mass in a very small neighborhood of *** enjoying its efficiency in posterior simulations,the shrinkage prior can lead to a nearly optimal posterior contraction rate and the variable selection consistency as the spike-and-slab *** numerical results show that under the posterior consistency,Bayesian methods can yield much better results in variable selection than the regularization methods such as LASSO and *** paper also establishes a BvM-type result,which leads to a convenient way of uncertainty quantification for regression coefficient estimates.

关键词： Bayesian variable selection absolutely continuous shrinkage prior heavy tail posterior consistency high-dimensional inference

Least Absolute Deviation Estimation of Autoregressive Conditional Duration Model

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Acta Mathematicae Applicatae Sinica 2011年第2期27卷 243-254页

作者： Wei Liu Hui-min Wang Min Chen Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Business School Hohai University Nanjing 210098 China Information Management Center of China Minsheng Banking Corp. Ltd. Beijing 100873 China

This paper studies the least absolute deviation estimation of the high frequency financial autoregressive conditional duration （ACD） model. The asymptotic properties of the estimator are studied given mild regularity conditions. Furthermore, we develop a Wald test statistic for the linear restriction on the parameters. A simulation study is conducted for the finite sample properties of our estimator. Finally, we give an empirical study of financial duration.

关键词： least absolute deviation estimation ACD model heavy tail

A NOTE ON ASYMPTOTIC BEHAVIOR FOR NEGATIVE DRIFT RANDOM WALK WITH DEPENDENT heavy-tailED STEPS AND ITS APPLICATION TO RISK THEORY

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Acta Mathematica Scientia 2007年第1期27卷 11-24页

作者：王定成苏淳 School of Applied Mathematics and School of Management University of Electronic Science and Technology of China Department of Statistics and Finance University of Science and Technology of China

In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process. Xn=-u＋∑j=-∞^∞ φn-jεj, where { ε, εn; -∞〈n〈＋∞} is a sequence of independent, identically distributed random variables with zero mean, u 〉 0 is a constant and the coefficients {φi; -∞〈i〈∞} satisfy 0〈 ∑j=-∞^∞ ｜jφj｜〈 ∞ . Under the conditions that the distribution function of ｜ε｜ has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{sup n≥0 （-qu＋∑j=-∞^∞ εj βnj）〉x} is discussed. Then the result is applied to ultimate ruin probability.

关键词： Dependent step heavy tail negative drift random walk tail balance condition ultimate ruin probability

Nonparametric inferences for kurtosis and conditional kurtosis

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Journal of Shanghai University(English Edition) 2009年第3期13卷 225-232页

作者：谢潇衡何幼桦 Department of Mathematics College of SciencesShanghai University

Under the assumption of strictly stationary process, this paper proposes a nonparametric model to test the kurtosis and conditional kurtosis for risk time series. We apply this method to the daily returns of S＆P500 index and the Shanghai Composite Index, and simulate GARCH data for verifying the efficiency of the presented model. Our results indicate that the risk series distribution is heavily tailed, but the historical information can make its future distribution light-tailed. However the far future distribution＇s tails are little affected by the historical data.

关键词： conditional probability density function (PDF) kernel estimate kurtosis conditional kurtosis heavy tail

Distributed Estimator of Market Beta under Extreme Conditions

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Journal of Applied Mathematics and Physics 2023年第11期11卷 3676-3701页

作者： Suyu Zhu School of Mathematics and Statistics Southwest University Chongqing China

Market beta is a measure of the volatility or systematic risk of a security or portfolio compared to the market as a whole. This paper considers the distributed estimation of market beta in the case of massive data, and obtains the consistency and asymptotic normality of the estimator. Further, simulations show the finite sample properties of this estimator.

关键词： heavy tail tail Dependence Distributed Statistical Inference Market Beta

Linear double autoregressive time series model and its conditional quantile inference

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Linear double autoregressive time series model and its condi...