基于CVaR与矩匹配方法的外汇储备资产配置动态随机优化模型

本文建立了一个动态的随机优化模型,对我国外汇储备在国际资产中的配置问题进行研究。采用基于矩匹配方法生成的情景树代表资产价格波动与币种间汇率变动的不确定性,将管理当局对于外汇储备安全性、流动性、收益性的要求统一纳入模型中,最终计算出外汇储备各资产的动态配置比例。结果表明,运用动态随机优化模型对我国外汇资产进行动态配置灵活、有效。     

基于多元t-分布的外汇期权市场风险非线性VaR度量模型

主要研究当汇率回报呈多元t-分布时,对于外汇期权非线性头寸的VaR(Value at Risk)度量的问题.在推导出多个外汇期权的投资组合的二次近拟的矩母函数表达式基础上,本文使用傅里叶变换、切比雪夫不等式、数值转换计算求出投资组合的VaR的值,并和基于多元正态分布Comish-Fisher模型以及基于Delta-正态模型计算所得的VaR值了进行比较.这种方法克服了厚尾分布的VaR计算的困难.     

图嵌入下稀疏低秩集成预测的多因子资产选择策略

面对金融市场的大量不确定性因素,如何合理选择有效的定价因子并构建科学的资产定价体系,一直是金融理论研究的核心问题之一。本文利用图嵌入的方法,基于稀疏表示和低秩表示策略,深度挖掘潜含在数据集中的内在结构,构建了能够同时揭示数据局部结构信息和全局结构信息的集成学习策略,以实现不同维度的多源数据融合。从CAPM和APT理论出发,通过集成预测的方法构建量化多因子资产选择模型,代表性地选择了卷积神经网络、梯度提升决策树、时间序列及支持向量机等模型进行单一预测,并通过稀疏低秩的图近似最小二乘回归集成策略进行优化。实证结果表明基于集成预测的稀疏低秩策略其资产选择能力更强,超额收益率更高。采用机器学习的非线性预测方法更有利于揭示金融系统的复杂特性。实证结论对投资组合管理具有重要指导意义。     

Some improved tail bounds for the sum of variables with geometric distribution

Abstract

In this paper, compared with the results in Janson (2018 Janson, S. 2018. Tail bounds for sums of geometric and exponential variables. Statistics & Probability Letters 135 (C):1–6. doi:10.1016/j.spl.2017.11.017.[Crossref] , [Google Scholar]), we provide some improved explicit bounds for the tail probabilities of the sum of independent geometric variables with their expectations and variances. Particularly, in some cases, we demonstrate that our bounds are sharper than the ones in Janson (2018 Janson, S. 2018. Tail bounds for sums of geometric and exponential variables. Statistics & Probability Letters 135 (C):1–6. doi:10.1016/j.spl.2017.11.017.[Crossref] , [Google Scholar]).     

Simple expressions for a bivariate chisquare distribution

The joint distribution of the estimated variances from a correlated bivariate normal distribution has a long history. However, its joint probability density function, conditional moments and product moments are only known as infinite series. In this paper, simpler expressions, mostly finite sums of elementary functions, are derived for these properties. Expressions are also derived for the joint moment generating function and the joint characteristic function.     

Design effect of randomized systematic sampling

In statistical practice, systematic sampling (SYS) is used in many modifications due to its simple handling. In addition, SYS may provide efficiency gains if it is well adjusted to the structure of the population under study. However, if SYS is based on an inappropriate picture of the population a high decrease of efficiency, i.e. a high increase in variance may result by changing from simple random sampling to SYS. In the context of two-stage designs SYS so far seems often in use for subsampling within the primary units. As an alternative to this practice, we propose to randomize the order of the primary units, then to select systematically a number of primary units and, thereafter, to draw secondary units by simple random sampling without replacement within the primary units selected. This procedure is more efficient than simple random sampling with replacement from the whole population of all secondary units, i.e. the variance of an adequate estimator for a total is never increased by changing from simple random sampling to randomized SYS whatever be the values associated by a characteristic with the secondary units, while there are values for which the variance decreases for the change mentioned. This result should hold generally, even if our proof, so far, is not complete for general sample sizes.     

Lévy‐based Modelling in Brain Imaging

Abstract. A substantive problem in neuroscience is the lack of valid statistical methods for non‐Gaussian random fields. In the present study, we develop a flexible, yet tractable model for a random field based on kernel smoothing of a so‐called Lévy basis. The resulting field may be Gaussian, but there are many other possibilities, including random fields based on Gamma, inverse Gaussian and normal inverse Gaussian (NIG) Lévy bases. It is easy to estimate the parameters of the model and accordingly to assess by simulation the quantiles of test statistics commonly used in neuroscience. We give a concrete example of magnetic resonance imaging scans that are non‐Gaussian. For these data, simulations under the fitted models show that traditional methods based on Gaussian random field theory may leave small, but significant changes in signal level undetected, while these changes are detectable under a non‐Gaussian Lévy model.     

A Fast Iterated Bootstrap Procedure for Approximating the Small-Sample Bias

This article proposes a fast approximation for the small sample bias correction of the iterated bootstrap. The approximation adapts existing fast approximation techniques of the bootstrap p-value and quantile functions to the problem of estimating the bias function. We show an optimality result which holds under general conditions not requiring an asymptotic pivot. Monte Carlo evidence, from the linear instrumental variable model and the nonlinear GMM, suggest that in addition to its computational appeal and success in reducing the mean and median bias in identified models, the fast approximation provides scope for bias reduction in weakly identified configurations.     

Some New Bounds on the Probability of Extinction of a Galton–Watson Process with Numerical Comparisons

Some new upper and lower bounds for the extinction probability of a Galton–Watson process are presented. They are very easy to compute and can be used even if the offspring distribution has infinite variance. These new bounds are numerically compared to previously discussed bounds. Some definite guidelines are given concerning when these new bounds are preferable. Some open problems are also discussed.     

A Generalized Poisson Distribution

Cumulative probabilities of a Poisson distribution can be written in terms of incomplete gamma function where the parameter of the gamma function is an integer. From this definition a new generalization of the Poisson distribution is obtained with two parameters. Asymptotic behavior of this distribution is shown to be normal. Some order properties of this distribution are also studied.