Short-time at-the-money skew and rough fractional volatility

The Black–Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time to maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian motion with Hurst parameter less than half. The fractional Brownian motion is correlated with a Brownian motion which drives the asset price process. We derive an asymptotic expansion of the implied volatility as the time to maturity tends to zero. For this purpose, we introduce a new approach to validate such an expansion, which enables us to treat more general models than in the literature. The local-stochastic volatility model is treated as well under an essentially minimal regularity condition in order to show such a standard model cannot be dynamically consistent to the power law.     

Growth Optimal Investment Strategy: The Impact of Reallocation Frequency and Heavy Tails

The strategy to maximize the long‐term growth rate of final wealth (maximum expected log strategy, maximum geometric mean strategy, Kelly criterion) is based on probability theoretic underpinnings and has asymptotic optimality properties. This article reviews the allocation of wealth in a two‐asset economy with one risky asset and a risk‐free asset. It is also shown that the optimal fraction to be invested in the risky asset (i) depends on the length of the basic return period and (ii) is lower for heavy‐tailed log returns than for light‐tailed log returns.     

村级财务治理新机制:村务(财务)监督委员会及其制度的学理解析——基于浙江武义县后陈村的调查

本文从浙江武义县后陈村财务监督个案出发,以财务学、制度经济学与法学为主要分析工具,对后陈村村务（财务）监督委员会组织及其制度进行学理解析,最终提出一般性结论与建议.     

The Limit Distribution of the Bootstrap for the Unit Root Test Statistic when the Residuals are Dependent

In this article, the unit root test for the AR(1) model with dependent residuals is considered. We adopt a bootstrap procedure to bootstrap the residuals with bootstrap sample size m less than the size n of the original sample. Under the assumptions that m → ∞ and m/n → 0, the convergence in probability of the bootstrap distribution function is established. Research supported by National Natural Science Foundation of China (No. 10471126)     

Poisson Regression for Clustered Data

We compare five methods for parameter estimation of a Poisson regression model for clustered data: (1) ordinary (naive) Poisson regression (OP), which ignores intracluster correlation, (2) Poisson regression with fixed cluster‐specific intercepts (FI), (3) a generalized estimating equations (GEE) approach with an equi‐correlation matrix, (4) an exact generalized estimating equations (EGEE) approach with an exact covariance matrix, and (5) maximum likelihood (ML). Special attention is given to the simplest case of the Poisson regression with a cluster‐specific intercept random when the asymptotic covariance matrix is obtained in closed form. We prove that methods 1–5, except GEE, produce the same estimates of slope coefficients for balanced data (an equal number of observations in each cluster and the same vectors of covariates). All five methods lead to consistent estimates of slopes but have different efficiency for unbalanced data design. It is shown that the FI approach can be derived as a limiting case of maximum likelihood when the cluster variance increases to infinity. Exact asymptotic covariance matrices are derived for each method. In terms of asymptotic efficiency, the methods split into two groups: OP & GEE and EGEE & FI & ML. Thus, contrary to the existing practice, there is no advantage in using GEE because it is substantially outperformed by EGEE and FI. In particular, EGEE does not require integration and is easy to compute with the asymptotic variances of the slope estimates close to those of the ML.     

Analysis of Instantaneous and Early Failures in Weibull Distribution

There are many situations in life testing experiment where an item fail instantaneously and hence the observed lifetime is reported as zero. The items that fail prematurely are called early failures. We propose a modified Weibull distribution as a suitable model to represent such situations by mixture of a singular distribution at zero and a two parameter Weibull distribution. We obtain the maximum likelihood estimates of the parameters and their asymptotic distributions. The methods are illustrated on drying of woods under different experiments and schedules reported by Vanmann (Research report, 1991:2).     

加权Hardy空间上算子序列的收敛性

设D为复平面C中的开单位圆盘，φ：D→D解析，ψ：D→C，Cψ，φ是H^2（β）上的加权复合算子，S是加权移位算子，该文通过讨论算子序列{S^＊nCψ，φS^n}n=1^∞与{S^＊nCψ，φ^＊S^n}n=1^∞的收敛性来研究H^2（β）上加权复合算子Cψ，φ的渐近Toeplitz性．     

非线性时序模型LM检验的两类临界值检验统计功效比较

本文基于模拟方法比较了不同非线性时序模型的LM检验的功效和规模，同时也考虑一般化线性检验BDS检验参与比较，目的在于探讨蒙特一卡洛渐近法检验与自举法（bootstrap）检验的两类临界值的统计功效何者更为有效。通过实证与对比分析，结果表明，当样本小于200或自回归系数接近单位根，或者线性性检验是ARCHT或BDS时，就可以考虑应用自举法临界值而非渐近临界值。而且还发现，BDS检验仅在一般性上优于LM检验。     

The conservative equal costs rule, the serial cost sharing rule and the pivotal mechanism: asymptotic welfare loss comparisons for the case of an excludable public project

We examine the asymptotic behavior of two strategyproof mechanisms discussed by Moulin for public goods – the conservative equal costs rule (CER) and the serial cost sharing rule (SCSR) – and compare their performance to that of the pivotal mechanism (PM) from the Clarke–Groves family. Allowing the individuals’ valuations for an excludable public project to be random variables, we show under very general assumptions that expected welfare loss generated by the CER, as the size of the population increases, becomes arbitrarily large. However, all moments of the SCSR’s random welfare loss asymptotically converge to zero. The PM does better than the SCSR, with its welfare loss converging even more rapidly to zero.     

Asymptotic behaviour of regression pre-test estimators with minimal Bayes risk

Pre-test estimators (PTE) are considered which are optimal under a Bayes risk among PTE with general measurable sets as “regions of significance” for the test statistic t associated with the estimate of a given regression coefficient. Asymptotic and some finite sample results are stated and numerical experiments are commented on.