CVaR HEDGING USING QUANTIZATION‐BASED STOCHASTIC APPROXIMATION ALGORITHM

In this paper, we investigate a method based on risk minimization to hedge observable but nontradable source of risk on financial or energy markets. The optimal portfolio strategy is obtained by minimizing dynamically the conditional value‐at‐risk (CVaR) using three main tools: a stochastic approximation algorithm, optimal quantization, and variance reduction techniques (importance sampling and linear control variable), as the quantities of interest are naturally related to rare events. As a first step, we investigate the problem of CVaR regression, which corresponds to a static portfolio strategy where the number of units of each tradable assets is fixed at time 0 and remains unchanged till maturity. We devise a stochastic approximation algorithm and study its a.s. convergence and weak convergence rate. Then, we extend our approach to the dynamic case under the assumption that the process modeling the nontradable source of risk and financial assets prices is Markovian. Finally, we illustrate our approach by considering several portfolios in connection with energy markets.     

无网格数值方法中的形函数研究

无网格法是近几年来发展的一种新的基于变分原理的数值计算方法,根据形函数构建和方程离散化方法的不同,分为不同的无网格法。文章主要讨论了移动最小二乘形函数的构建方法、性质。通过对曲线和曲面拟合算例的研究表明:权函数的选择、节点数目、影响域大小、基函数的选取等对形函数的精度和稳定性都有影响,通过数值实验给出了各参数的参考值。     

拉格朗日插值多项式于平方收敛意义下的收敛逼近阶

本文得到了以 Legendre 多项式及以 Tchebycheff 多项式的导数的零点为插值结点组的拉格朗日插值多项式于平方收敛意义下的收敛速度。     

Bootstrap unit root tests in panels with cross-sectional dependency

We apply bootstrap methodology to unit root tests for dependent panels with N cross-sectional units and T time series observations. More specifically, we let each panel be driven by a general linear process which may be different across cross-sectional units, and approximate it by a finite order autoregressive integrated process of order increasing with T. As we allow the dependency among the innovations generating the individual series, we construct our unit root tests from the estimation of the system of the entire N cross-sectional units. The limit distributions of the tests are derived by passing T to infinity, with N fixed. We then apply bootstrap method to the approximated autoregressions to obtain critical values for the panel unit root tests, and establish the asymptotic validity of such bootstrap panel unit root tests under general conditions. The proposed bootstrap tests are indeed quite general covering a wide class of panel models. They in particular allow for very general dynamic structures which may vary across individual units, and more importantly for the presence of arbitrary cross-sectional dependency. The finite sample performance of the bootstrap tests is examined via simulations, and compared to that of commonly used panel unit root tests. We find that our bootstrap tests perform relatively well, especially when N is small.     

A GM(1,1)–Markov chain combined model with an application to predict the number of Chinese international airlines

In this paper, we propose a new dynamic analysis model which combines the first-order one-variable grey differential equation model (abbreviated as GM(1,1) model) from grey system theory and Markov chain model from stochastic process theory. We abbreviate the combined GM(1,1)–Markov chain (MC) model as MCGM(1,1) model. This combined model takes advantage of the high predictable power of GM(1,1) model and at the same time take advantage of the prediction power of Markov chain modelling on the discretized states based on the GM(1,1) modelling residual sequence. For prediction accuracy improvements, Taylor approximation is applied to MCGM(1,1) model. We call the improved version as T-MCGM(1,1) model. As an example, we use the statistical data of the number of Chinese international airlines from 1985 to 2003 for a validation of the effectiveness of the T-MCGM(1,1) model.     

中国市场利率期限结构的静态估计

利率期限结构是资产定价、金融产品设计、保值和风险管理、套利以及投资等的基础。因此 ,对利率期限结构的估计是金融工程领域一个十分基础的工作。本文则是在这方面进行的一个尝试性研究工作。对利率期限结构的估计可以有许多方法 ,其中包括息票剥离法(bootstrapmethod)和样条估计法(splineapproximation)。本文则同时利用这两种方法对中国2001-2002的利率期限结构进行一个静态的估计 ,比较两种估计方法的静态估计结果并在此基础上分析中国利率期限结构的变化特征     

Tourism in ASEAN-5: A novel panel unit-root test for shocks persistence with gradual structural breaks and common factors

This study investigates whether shocks to tourist arrivals in Indonesia, Malaysia, Philippines, Singapore, and Thailand (ASEAN-5) are permanent or transitory, given the frequent and severe external shocks experienced by the tourism industry. Using monthly data from 2000 to 2019, we employ a novel panel unit-root test that controls for cross-correlations, multiple gradual structural breaks, and other nonlinearities present in the data to assess the stationarity properties of tourist arrivals. Additionally, we apply a panel unit-root test that controls for cross-correlations and allows for abrupt structural changes for robustness. The empirical findings reveal that shocks to tourist arrivals in the ASEAN-5 countries exert persistent effects. Our results demonstrate nonstationarity within the series, illuminated by our careful consideration of both gradual and abrupt structural breaks. This finding underscores the necessity for policy interventions to mitigate the impact of adverse shocks on the tourism industry.     

基于快速OPAST算法的直扩信号PN码序列估计

在直接序列扩频（DSSS）通信对抗系统中,伪码（PN）序列估计是一个重要的研究课题。针对在某些情况下权值向量不收敛的问题,提出了一种基于快速正交投影逼近子空间跟踪（OPAST）算法和滑动窗技术的直扩信号PN码序列估计算法,对非同步接收DSSS信号按照宽窗口分段,利用快速OPAST算法提取主特征向量,滑动窗技术实现码同步。该算法迭代权值向量具有正交性以及良好的收敛性,同时解决了常见相位模糊问题。算法具有较低复杂度,数据存储量少,易于硬件实现与实时处理。仿真结果表明,在-10 dB的较低信噪比背景环境中,该快速OPAST算法可以正确有效地估计出PN码序列。     

On a general class of one-factor models for the term structure of interest rates

We propose a general one-factor model for the term structure of interest rates which based upon a model for the short rate. The dynamics of the short rate is described by an appropriate function of a time-changed Wiener process. The model allows for perfect fitting of given term structure of interest rates and volatilities, as well as for mean reversion. Moreover, every type of distribution of the short rate can be achieved, in particular, the distribution can be concentrated on an interval. The model includes several popular models such as the generalized Vasicek (or Hull-White) model, the Black-Derman-Toy, Black-Karasinski model, and others. There is a unified numerical approach to the general model based on a simple lattice approximation which, in particular, can be chosen as a binomial or -nomial lattice with branching probabilities .     

How accurate is the integrated vendor–buyer continuous model?

The classic single-item, deterministic-demand, integrated vendor–buyer model is revisited. The decision problem may also be viewed as that of one centralized firm, dealing with a two-level EOQ-like supply chain with finite production rates. It is sought to optimize the production lot-size and the integral number of its shipments, in equal batches, from the vendor to the buyer. While the problem calls for discrete optimization techniques, we introduced a continuous model where one can take derivatives with respect to both variables. In this short paper, we establish a 98.5% lower bound on the accuracy of this continuous model.