On Mixed and Compound Mixed Poisson Distributions

Recursive formulae are derived for the evaluation of the t-th order cumulative distribution function and the t-th order tail probability of compound mixed Poisson distributions in the case where the derivative of the logarithm of the mixing density can be written as a ratio of polynomials. Also, some general results are derived for the evaluation of the t-th order moments of stop-loss transforms. The recursions can be applied for the exact evaluation of the probability function, distribution function, tail probability and stop-loss premium of compound mixed Poisson distributions and the corresponding mixed Poisson distributions. Several examples are also presented.     

Bayesian Comparison of ARIMA and Stationary ARMA Models

Time series analysts have long been concerned with distinguishing stationary "generating processes" from processes for which differencing is required to induce stationarity. In practical applications, this issue is addressed almost invariably through formal hypothesis testing. In this paper, we explore some aspects of the Bayesian approach to the problem, leading to the calculation of posterior odds ratios. Interesting features arise in the simplest possible variant of the problem, where a choice has to be made between a random walk and a stationary first order autoregressive model. We discuss in detail the analysis of this case, and also indicate how our approach extends to the more general comparison of an ARIMA model with a stationary competitor.     

Hedge fund return higher moments over the business cycle

We investigate how macroeconomic and financial uncertainty impacts the behavior of hedge fund strategy higher moments—i.e., co-skewness and co-kurtosis—and their respective cross-sectional dispersions. Consistent with theoretical models, we find that strategy managers trade off these two higher moments when building optimal portfolios. Moreover, these trade-offs depend on the kind of strategy. Our experiments show that the VIX and its conditional variance are the most important factors affecting higher moment risk in the hedge fund industry. They also reveal that the behavior of hedge fund strategies is very asymmetric depending on the phase of the business cycle. In contrast to studies which rely on the mean-variance setting, we find that systemic risk—as measured by the cross-sectional dispersions of higher moments—tends to decrease in the low regime. The indicators of market volatility play a decisive role to explain this decline in systemic risk.     

Investor attention,ETF returns,and country-specific factors

Using the data of 47 single-country exchange-traded funds (ETFs) traded in the U.S. from 36 countries during 2004–2017, this research examines the impact of investor attention proxied by Google Search Volume Index and home country-specific factors on different quantile of their returns. Evidence first shows that compared with U.S. investor attention, home country investor attention largely correlates with low to medium ETF returns, supporting the attention-induced price pressure hypothesis. Second, home country-specific factors significantly affect ETF returns at different conditional quantiles. We also find that investors prefer investing in a country with strong similarity to that of the U.S., supporting the cross-country information asymmetry hypothesis. Third, an intervening effect of home country-specific factors exists on the relationship between U.S. investor attention and ETF returns. These findings should help government authorities find appropriate strategies to attract foreign investment and upgrade the value of their capital market as well as provide a reference on efficiency for equity investors.     

SCENARIO GENERATION FOR OPERATIONAL RISK

Operational risk is an increasingly important area of risk management. Scenarios are an important modelling tool in operational risk management as alternative viable methods may not exist. This can be due to challenging modelling, data and implementation issues, and other methods fail to take into account expert information. The use of scenarios has been recommended by regulators; however, scenarios can be unreliable, unrealistic and fail to take into account quantitative data. These problems have also been identified by regulators such as Basel, and presently little literature exists on addressing the problem of generating scenarios for operational risk. In this paper we propose a method for generating operational risk scenarios. We employ the method of cluster analysis to generate scenarios that enable one to combine expert opinion scenarios with quantitative operational risk data. We show that this scenario generation method leads to significantly improved scenarios and significant advantages for operational risk applications. In particular for operational risk modelling, our method leads to resolving the key problem of combining two sources of information without eliminating the information content gained from expert opinions, tractable computational implementation for operational risk modelling, improved stress testing, what‐if analyses and the ability to apply our method to a wide range of quantitative operational risk data (including multivariate distributions). We conduct numerical experiments on our method to demonstrate and validate its performance and compare it against scenarios generated from statistical property matching for comparison. Copyright © 2013 John Wiley & Sons, Ltd.     

I.J. Bienaymé [1796–1878]: Criticality,Inequality, and Internationalization*

Two striking contributions of Bienaymé to mathematical statistics: (1) a completely correct statemet of the Criticality Theorem for simple branching processes in 1845; and (2) the derivation of the Bienaymé-Chebyshev Inequality, are revisited on the 200th anniversary of his birth. We use writings and archival materials available since the note of Heyde & Seneta (1972) to present a fuller biographical picture. Bienaymé's connections with Buniakovsky and Chebyshev are elucidated, and this role in furthering Chebyshev's international contacts outlined. A concluding section illuminates Bienaymé's understanding of the linear regression of one random variable on another in an actuarial context of random shocks.     

Intra-industry spillovers and innovation: An econometric analysis at the firm level

This paper studies spillover effects of innovation at the firm level and the comparability of generalized method of moments (GMM) estimators with maximum likelihood estimators of the earlier studies. Two sources of spillovers are identified, i.e. intra-industry R&D expenditure and intra-industry innovation output. This paper estimates a negative R&D spillover effect and a positive output spillover effect. Because of the substitution effect of intra-industry R&D spillovers, the elasticity of patent with respect to firm's own R&D expenditure is greater than those estimated in the earlier studies. With GMM, individual effects are incorporated into the models either by developing proxies for them or attempting to eliminate them.     

A Simulation Approach to Nonparametric Empirical Bayes Analysis

We deal with general mixture of hierarchical models of the form m(x) = f_øf(x |θ) g (θ)dθ , where g(θ) and m(x) are called mixing and mixed or compound densities respectively, and θ is called the mixing parameter. The usual statistical application of these models emerges when we have data x_i, i = 1,…,n with densities f(x_i|θ_i) for given θ_i, and the θ₁ are independent with common density g(θ) . For a certain well known class of densities f(x |θ) , we present a sample-based approach to reconstruct g(θ) . We first provide theoretical results and then we use, in an empirical Bayes spirit, the first four moments of the data to estimate the first four moments of g(θ) . By using sampling techniques we proceed in a fully Bayesian fashion to obtain any posterior summaries of interest. Simulations which investigate the operating characteristics of our proposed methodology are presented. We illustrate our approach using data from mixed Poisson and mixed exponential densities.     

银行业结构对城乡收入差距影响研究——基于新结构经济学最优金融结构理论视角

城乡收入差距关乎社会公平、牵系经济的可持续发展。基于2009—2014年我国31个省市自治区的面板数据,构建了动态面板模型,运用广义矩估计方法（GMM)就中小银行发展对城乡收入差距的影响及其作用渠道进行了研究。结果表明,中小银行发展对城乡收入差距的直接效应是扩大城乡收入差距,但通过中小企业发展渠道产生的间接效应缩小了城乡收入差距;且中小企业发展主要通过就业效应和经济增长效应提高农村居民收入,缩小城乡收入差距,且就业效应要大于经济增长效应。政策含义：优化金融结构中的银行业结构,使得中小银行发展推动中小企业发展释放就业效应和经济增长效应,抑制城乡收入差距的扩大。     

On measuring skewness and kurtosis

The paper considers some properties of measures of asymmetry and peakedness of one dimensional distributions. It points to some misconceptions of the first and the second Pearson coefficients, the measures of asymetry and shape, that frequently occur in introductory textbooks. Also it presents different ways for obtaining the estimated values for the coefficients of skewness and kurtosis and statistical tests which include them.