Is nitrogen oxides emissions spatially correlated in a Chinese context? What is the relationship between nitrogen oxides emission levels and fast-growing economy/urbanization? More importantly, what environmental preservation and economic developing policies should China’s central and local governments take to mitigate the overall nitrogen oxides emissions and prevent severe air pollution at the provincial level in specific locations and their neighboring areas? The present study aims to tackle these issues. This is the first research that simultaneously studies the nexus between nitrogen oxides emissions and economic development/urbanization, with the application of a spatial panel data technique. Our empirical findings suggest that spatial dependence of nitrogen oxides emissions distribution exists at the provincial level. Through the investigation of the existence of an environmental Kuznets curve (EKC) embedded within the Stochastic Impacts by Regression on Population, Affluence, and Technology (STIRPAT) framework, we conclude something interesting: an inverse N-shaped EKC describes both the income-nitrogen oxides nexus and the urbanization-nitrogen oxides nexus. Some well-directed policy advice is provided to reduce nitrogen oxides in the future. Moreover, these results contribute to the literature on development and pollution.

Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE) model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function) in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study.

The digital economy can change the proportions and types of production factors, gradually replace traditional backward production factors, reconstruct the division of labor and cooperation system, and improve productivity, which is an important basis for balanced and sufficient development. This paper measures the comprehensive level of the digital economy and balanced and sufficient development, by using Chinese provincial panel data from 2013 to 2021, and uses the panel fixed effect model, mediation effect model, and spatial econometric model to examine the digital economy’s effect on balanced and sufficient development as well as the digital economy’s mechanism. The results show that the digital economy has significantly promoted balanced and sufficient development, though there are obvious regional heterogeneity and spatial spillover effects, and the relevant conclusions are still valid after an endogenous treatment and a robustness test. The total factor productivity is an important mechanism for the digital economy to affect balanced and sufficient development.

In financial markets, there exists long-observed feature of the implied volatility surface such as volatility smile and skew. Stochastic volatility models are commonly used to model this financial phenomenon more accurately compared with the conventional Black-Scholes pricing models. However, one factor stochastic volatility model is not good enough to capture the term structure phenomenon of volatility smirk. In our paper, we extend the Heston model to be a hybrid option pricing model driven by multiscale stochastic volatility and jump diffusion process. In our model the correlation effects have been taken into consideration. For the reason that the combination of multiscale volatility processes and jump diffusion process results in a high dimensional differential equation (PIDE), an efficient finite element method is proposed and the integral term arising from the jump term is absorbed to simplify the problem. The numerical results show an efficient explanation for volatility smirks when we incorporate jumps into both the stock process and the volatility process.

A linearized compact finite difference scheme is constructed for solving the fractional neutral parabolic differential equation with proportional delay. By the energy method, the unconditional stability of the scheme is proved, and the convergence order of the scheme is proved to be O(τ2-α+h4). A numerical test is also conducted to validate the accuracy and efficiency of the numerical algorithm.

This paper studies the equity premium and option pricing under the general equilibrium framework taking into account stochastic volatility. We establish analytical expressions for the equity premium and pricing kernel of the stock process. Moreover, the equilibrium option pricing formula is derived by the Fourier transformation method. Numerical results show that our model is superior to the previous model with constant volatility in explaining some financial phenomena, such as negative variance risk premium, implied volatilities and negative skewness risk premium. As the price of the underlying asset is modeled as the exponential of the Lévy process with stochastic volatility, our model is more general than the existing equilibrium pricing models.