Estimation using plug-in of the stationary distribution and Shannon entropy of continuous time Markov processes

A natural way to deal with the uncertainty of an ergodic finite state space Markov process is to investigate the entropy of its stationary distribution. When the process is observed, it becomes necessary to estimate this entropy.We estimate both the stationary distribution and its entropy by plug-in of the estimators of the infinitesimal generator. Three situations of observation are discussed: one long trajectory is observed, several independent short trajectories are observed, or the process is observed at discrete times. The good asymptotic behavior of the plug-in estimators is established. We also illustrate the behavior of the estimators through simulation.     

基于可变强度跳跃-GARCH模型的资产价格跳跃行为分析——以中国上市公司股票市场数据为例

近年来,美国金融危机、欧债危机、地震等突发事件不断冲击着我国金融市场,各类资产价格频繁出现大幅跳动,收益风险短期内急剧扩大。鉴于此,本文构建了门限效应下状态变量依赖自回归强度跳跃-GARCH模型（简称TSD-ARJI-GARCH模型）来探讨股票资产价格随时间平滑波动和大幅度跳跃的双重特征。该模型扩展了现有可变强度跳跃-GARCH模型,克服了片面强调内生或外生因素的局限性,既允许跳跃强度受单个资产异质因素的内生驱动,以刻画跳跃变化的时变性及集聚性,也考虑了外部状态变量影响的门限效应。通过对不同类型中国上市公司股票市场数据的实证分析,验证了该模型对各类上市公司股票资产价格跳跃特征都具有较好的辨别和预测能力,可为动态监管金融资产的跳跃风险提供理论依据。     

跳过程下的公司证券定价和最优资本结构

由于几何布朗运动不能反映复杂经济背景下的资产价值动态,本文以双指数跳扩散过程作为资产价值过程来研究公司证券定价和最优资本结构问题。本文主要结果是：运用均衡定价的方法给出了公司证券的定价并获得了公司资本价值的解析解。通过比较静态分析揭示了跳风险对企业资本价值、最优资本结构、收益率差价等都具有显著的影响。与几何布朗运动相比,跳风险降低了公司价值和债券价值以及公司最优杠杆率,同时增加了债券的收益率差价和股权价值。     

沪深300股指期货上市对现货市场连续波动和跳跃波动的影响

本文采用跳-扩散随机波动率模型研究沪深300股指期货上市对现货市场波动的影响。通过MCMC方法估计模型参数,对股指期货上市前后指数连续波动和跳跃特征进行比较分析,并与股指期货各指标作比较。研究发现,股指期货的上市确实起到了稳定现货市场的作用,上市短期内现货市场波动增大,随着时间增加现货市场波动逐渐降低,但是这一稳定效果主要体现在指数波动率的连续部分。股指期货上市后,指数连续波动向均值回归速度加快,并呈现出逐渐降低的趋势;“杠杆效应”在经历短暂的消失后逐渐显现;指数跳跃波动在总波动中所占比重较高,但随着交易时间增加,指数平均跳跃次数和跳跃波动所占比重逐渐降低。     

The estimation for Lévy processes in high frequency data

In this article, a generalized Lévy model is proposed and its parameters are estimated in high-frequency data settings. An infinitesimal generator of Lévy processes is used to study the asymptotic properties of the drift and volatility estimators. They are consistent asymptotically and are independent of other parameters making them better than those in Chen et al. (2010 Chen, S. X., Delaigle, A., Hall, P. (2010). Nonparametric estimation for a class of Lévy processes. Journal of Econometrics 157:257–271.[Crossref], [Web of Science ®] , [Google Scholar]). The estimators proposed here also have fast convergence rates and are simple to implement.     

我国银行间同业拆借利率的动态研究———基于跳跃 扩散 机制转换模型的实证分析

针对我国短期利率易受政策影响,波动较大并存在结构变化等特点,构建了跳跃 扩散 机制转换模型,同时考察了银行间 7 天同业拆借利率的波动、跳跃和结构变化三种效应,发现我国同业拆借利率不仅具有均值回归特性而且还存在明显的跳跃与机制转换,并且该模型 比其嵌套的受限模型表现更佳． 在高波动状态下利率波动的水平效应和 ARCH 效应可以忽略; 低波动状态下,水平效应可以忽略． 另外,跳跃具有聚类效应,高( 低) 的跳跃概率和高( 低)状态概率对应着高( 低) 利率和较高( 低) 的波动率,跳跃主要发生在高状态机制下,低状态机 制下发生跳跃的可能性很小．     

我国银行间同业拆借利率的动态研究——基于跳跃-扩散-机制转换模型的实证分析

针对我国短期利率易受政策影响,波动较大并存在结构变化等特点,构建了跳跃-扩散-机制转换模型,同时考察了银行间7天同业拆借利率的波动、跳跃和结构变化三种效应,发现我国同业拆借利率不仅具有均值回归特性而且还存在明显的跳跃与机制转换,并且该模型比其嵌套的受限模型表现更佳.在高波动状态下利率波动的水平效应和ARCH效应可以忽略...     

两类系统的逐点伪轨跟踪性研究

本文主要研究提升系统和逆极限系统,证明了如果基础系统具有逐点伪轨跟踪性,则其提升系统也具有逐点伪轨跟踪性;如果每个fi具有逐点伪轨跟踪性,则诱导映射也具有逐点伪轨跟踪性。     

The Effect of Timing on Jump Bidding in Ascending Auctions

We investigate the role of timing in ascending auctions under the premise that time is a valuable resource. Traditional models of the English auction ignore timing issues by assuming that the auction occurs instantaneously. However, when auctions are slow, as Internet auctions used for procurement often are, there are significant opportunity or monitoring costs to bidders, and the choice of the size of the jump bid becomes a strategic decision. We study the choice in the experimental laboratory by systematically varying the opportunity costs associated with fast bidding. When time is more valuable bidders respond by choosing larger jump bids. Surprisingly, the economic performance of the auction is not significantly affected. We develop a simple model of ascending auctions with impatient bidders that provides insights into the effect jump bids have on auction performance.     

LAN property for an ergodic diffusion with jumps

In this paper, we consider a multidimensional ergodic diffusion with jumps driven by a Brownian motion and a Poisson random measure associated with a compound Poisson process, whose drift coefficient depends on an unknown parameter. Considering the process discretely observed at high frequency, we derive the local asymptotic normality (LAN) property.