On the first hitting time density for a reducible diffusion process

In this paper, we study the classical problem of the first hitting time density to a moving boundary for a diffusion process, which satisfies the Cherkasov condition, and hence, can be reduced to a standard Wiener process. We give two complementary (forward and backward) formulations of this problem and provide semi-analytical solutions for both. By using the method of heat potentials, we show how to reduce these problems to linear Volterra integral equations of the second kind. For small values of t, we solve these equations analytically by using Abel equation approximation; for larger t we solve them numerically. We illustrate our method with representative examples, including Ornstein–Uhlenbeck processes with both constant and time-dependent coefficients. We provide a comparison with other known methods for finding the hitting density of interest, and argue that our method has considerable advantages and provides additional valuable insights. We also show applications of the problem and our method in various areas of financial mathematics.     

Prediction of volatility based on realized-GARCH-kernel-type models: Evidence from China and the U.S.

We propose three Realized-GARCH-Kernel-type models which do not make the distribution assumptions on the return disturbance terms. We use this type of model to predict the return volatilities of the 50ETF in China and the S&P500 index in the U.S. The semiparametric kernel density estimator of our models, which captures the skewness, asymmetry and fat-tail of financial assets, performs well both statistically and economically. Our models have more predictive power than other eight comparable volatility models that need to pre-specify the distribution of the disturbance terms. Our results are robust to eight measures of realized volatility. Using option straddle strategies, we show that our models generate larger trading profits and greater Sharpe ratios than the other competing models.     

Persistence of cities: Evidence from China

Using data from the Qing dynasty, we investigate the long‐run impact of early development on today's living standards in China. We use city‐level population density in 1776 as a measure of early economic prosperity, and examine how it is associated with today's development indicators such as the average night light density, GDP per capita, average years of schooling, and trade openness. We find that cities which were more prosperous during the Qing dynasty are now also brighter, richer, more educated, and more open.     

Patent enforcement across 51 countries – Patent enforcement index 1998–2017

Indices are central for comparing the strength of patent systems across countries in international business research, intellectual property management and policymaking. However, existing approaches rely on book laws while most variance across countries emerges from enforcement. We address this weakness and present the Patent Enforcement Index which tracks differences in patent enforcement for 51 countries between 1998 and 2017. We utilize novel firm-level enforcement data and extend the conceptual framework of the patent systems strength index provided by Papageorgiadis et al. (2014). The new index reveals previously uncaptured volatility in patent enforcement and can be decomposed into three topical sub-indices.     

Local corporate misconduct and local initial public offerings

This paper investigates the cost of going public through initial public offerings (IPOs) for firms located in regions with significant fraud density. We find that companies in regions with a high proportion of nearby firms that have committed corporate misconduct have more pronounced underpricing, experience higher post-IPO stock return volatility, and are more likely to withdraw their offerings. Overall, our results show that local corporate misconduct is associated with the pricing of IPOs, and the breach of trust is related to costly IPOs for newcomers.     

Do deeper regional trade agreements enhance international technology spillovers?

We examine whether regional trade agreements (RTAs) enhance international technology spillovers using a panel of patent citation data for 114 countries/regions for the period 1991–2007. We use patent citations as a proxy for technology spillovers. The focus of this study is on whether the depth of regional integration matters for technology spillovers among member countries/regions of RTAs. The depth of integration is measured by the extent to which an RTA includes legal obligations outside the current mandate of the World Trade Organization. We find that the depth of integration actually influences technology spillovers and that a deeper integration in a broad sense has a greater impact on technology spillovers than do technology‐related provisions.     

The rise of 3D printing and the role of user firms in the U.S.: evidence from patent data

3D printing has been heralded as one of the key technologies for the Fourth Industrial Revolution but empirical analysis is still sparse. This paper provides empirical evidence by proposing a robust approach to identifying 3D printing inventions. Findings indicate the inventive activity has been rapidly growing since 2011 and is mainly led by user firms. The development of 3D printing has taken place in a variety of industrial sectors, not merely a specific sector. This implies 3D printing can be considered as a general purpose technology. Interestingly, the diffusion patterns of 3D printing vary across technological categories. User firms are divided into incumbent and new firms to examine how patent activities vary by the type of firm and time. Incumbent firms exploit 3D printing earlier than new firms do but new firms tend to enter into 3D printing space more than incumbent firms after the technology becomes prevalent.     

Response to the Letter to the Editor on ‘On Quantile-based Asymmetric Family of Distributions: Properties and Inference’

Rubio (2020) points out an identification problem for the four-parameter family of two-piece asymmetric densities introduced by Nassiri & Loris (2013). This implies that statistical inference for that family is problematic. Establishing probabilistic properties for this four-parameter family however still makes sense. For the three-parameter family, there is no identification problem. The main contribution in Gijbels et al. (2019a) is to provide asymptotic results for maximum likelihood and method-of-moments estimators for all members of the three-parameter quantile-based asymmetric family of distributions.     

专利密集型产业研究中的自动标引系统

对海量专利进行标引从而找到每件专利和国民经济行业的对应关系是专利密集型产业研究中最关键的环节。详细阐述了数据清洗、机读分类号数据格式、机读分类号到国际专利分类号的格式转换,在此基础上实现了专利自动标引系统,可对海量专利进行快速、批量化的自动标引。结果表明,该系统很好的满足了专利密集型产业研究项目的需求。     

A note on the distribution of the product of zero‐mean correlated normal random variables

The problem of finding an explicit formula for the probability density function of two zero‐mean correlated normal random variables dates back to 1936. Perhaps, surprisingly, this problem was not resolved until 2016. This is all the more surprising given that a very simple proof is available, which is the subject of this note; we identify the product of two zero‐mean correlated normal random variables as a variance‐gamma random variable, from which an explicit formula for the probability density function is immediate.