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Accuracy and Consistency of the Explicit-Invariant Energy Quadratization Approach for the Cahn-Hilliard Equation

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Journal of Mathematical research with Applications 2025年第1期 84-104页

作者： Jun ZHANG Fangying SONG Yu ZHANG Computational Mathematics research center Guizhou University of Finance and Economics school of mathematics and statistics Guizhou University of Finance and Economics school of Mathematics and Stastistics Fuzhou University

It is well known that the explicit-invariant energy quadratization (EIEQ) approach can generate fully decoupled, linear and unconditionally energy-stable numerical schemes, so it is favored by many researchers. However, the undeniable fact is that the numerical method obtained by EIEQ approach preserves the “modified” energy law instead of the original *** is mainly due to the introduction of some auxiliary variables in EIEQ scheme, and the truncation error will make the auxiliary variables deviate from the original definition in the process of numerical calculation. The primary objective of this paper is to address this gap by providing the accuracy and consistency of the EIEQ method in the context of the CahnHilliard equation. We introduce a relaxation technique for auxiliary variables and construct two numerical schemes based on EIEQ. The analysis results show that the newly constructed schemes are not only unconditionally energy stable, linear and fully decoupled, but also can effectively correct the errors introduced by auxiliary variables and follow the original energy ***, several 2D and 3D numerical examples illustrate the accuracy and efficiency of the newly constructed numerical schemes.

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How do“gatekeepers”affect credit risk?

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Journal of Management Science and Engineering 2021年第3期6卷 295-311页

作者： Xu Li Xingtong Zhang Yinggang Zhou Faculty of Business and economics University of Hong KongHong KongBeijing100872China school of finance Renmin University of ChinaBeijing100872China center for macroeconomic research&department of finance at school of economics and Wang Yanan Institute for Studies in EconomicsXiamen UniversityXiamen361005China

This study investigates the relationship between auditor tenure and credit default swap(CDS)spreads of *** based on quantile *** allowing for common determinants of CDS spreads,auditor tenure exerts both statistically and economically significant additional impacts on the CDS ***,there are differential effects of common CDS spread determinants and auditor *** common determinants of CDS spreads(e.g.,leverage,volatility,risk free rate,credit ratings,and earnings)have monotonically increasing impacts when CDS spreads(and their changes)are increasingly higher,auditor tenure primarily has the impact when CDS spreads are of low or median levels for less risky firms.

关键词： Credit default swaps Auditor tenure Information Quantile regression

Empirical Likelihood-based Inferences in Varying Coefficient Models with Missing Data

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Acta Mathematicae Applicatae Sinica 2015年第3期31卷 823-840页

作者： Xiao-hui LIU school of Statistics Jiangxi University of Finance and Economics research center of Applied Statistics Jiangxi University of Finance and Economics

In this paper, we consider the empirical likelihood-based inferences for varying coefficient models Y = X^τα（U）＋ ε when X are subject to missing at random. Based on the inverse probability-weighted idea, a class of empirical log-likelihood ratios, as well as two maximum empirical likelihood estimators, are developed for α（u）. The resulting statistics are shown to have standard chi-squared or normal distributions *** studies are also constructed to illustrate the finite sample properties of the proposed statistics.

关键词： varying coefficient models missing at random empirical likelihood maximum empirical likelihood estimator

DYNAMIC PRICE MODEL BASED ON TRANSMISSION DELAY——PETROLEUM PRICE FLUCTUATION IN CHINA

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Journal of Systems Science & Complexity 2014年第3期27卷 507-523页

作者： LIU Yifang WANG Yue QIAO Heng economics school Central University of Finance and Economics research center for Climate and Energy finance CUFE school of Management University of Chinese Academy of Sciences China Development Bank

Petroleum is a kind of fundamental energy resource. Its price fluctuation transmits from upper-stream industry to the lower-stream industry as the production factors price changes. And this leads to the price changes of final consumption. Meantime, due to the cycle of industrial chain, the price changes of lower-stream industry also affect the upper-stream industry in return. This price transmission path is quite complicated. Firstly, it includes both direct and indirect paths; secondly, the transmission process is accompanied with time delay. The traditional input-output price model based on cost-push theory can efficiently solve the first problem when estimating the impact of price fluctuation on the whole price system. However, it neither reflects the dynamic characteristics of price transmission with time nor solves the second problem. To solve this problem, this paper uses the directed weighted network to describe the price transmission among industrial sectors by taking the time-dimension into account, and dynamic price transmission network model is constructed. This model not only describes transmission time delay more accurately, but also calculates the price fluctuation dynamically. On this basis, by utilizing the 2007 Chinese input-output table, this paper conducts empirical analysis on the impact of petroleum price fluctuation on other sectors. The empirical results indicate that the price fluctuation transmission mainly depends on two factors, the orice reaction period Tk and the consumption relationship with petroleum aik. 1） If t 〈 Tk, then the price change of sector k at period t △pkt = 0, the petroleum price fluctuation has not transmitted to the sector k, so the price of sector k remains unchanged. 2） If t 〉 Tk, then Apt 〉 0, and the greater aik, the higher price change rate. 3） If t →∞, it is the same with that in traditional input-output price model. So it can be clearly seen that dynamic price transmission network model is more general than the t

关键词： Directed weighted network input-output price model petroleum price transmission timedelay.

AN ACCURATE BINOMIAL MODEL FOR PRICING AMERICAN ASIAN OPTION

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Journal of Systems Science & Complexity 2014年第5期27卷 993-1007页

作者： LIU Jian WU Weixing XU Jingfeng ZHAO Haijian school of Insurance Central University of Finance and Economics research center for Applied finance School of Banking and FinanceUniversity of International Business and Economics China Institute for Actuarial Science Central University of Finance and Economics Bosera Asset Management Co. Ltd.

This paper presents simple and fast algorithms for computing very tight upper and lower bounds on the prices of American Asian options in the binomial *** authors choose two types sets of the actual arithmetic average prices,instead of the simulated values in other existing models,as the representative average prices at each node of the binomial *** approach simplifies effectively the computation and reduces the error caused by the linear *** results show that the approach produces accurate upper and lower bounds compared to the other existing methods based on the binomial tree.

关键词： Asian option binomial tree option pricing

Pricing Credit Spread Option with Longstaff-Schwartz and GARCH Models in Chinese Bond Market

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Journal of Systems Science & Complexity 2015年第6期28卷 1363-1373页

作者： ZHOU Rongxi DU Sinan YU Mei YANG Fengmei school of economics and Management Beijing University of Chemical Technology research center for Applied finance School of Finance and Banking University of International Business and Economics school of Science Beijing University of Chemical Technology

This paper investigates the mean-reversion and volatile of credit spread time series by using regression and time series analysis in Chinese bond market. Then the Longstaff-Schwartz model and GARCH model are applied to price credit spread put option. The authors compare the features of these two models by employing daily bond prices of government bonds and corporate bonds for the period 2010–2012 in Chinese bond market. The proposed results show that the higher the credit ratings of the corporate bonds are, the lower the prices of the credit spread options are.

关键词： Credit spread option Longstaff-Schwartz model GARCH model pricing

On Optimal Mean-Field Control Problem of Mean-Field Forward-Backward Stochastic System with Jumps Under Partial Information

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Journal of Systems Science & Complexity 2017年第4期30卷 828-856页

作者： ZHOU Qing REN Yong WU Weixing school of Science Beijing University of Posts and Telecommunications department of Mathematics Anhui Normal University research center of Applied finance and school of finance and Banking University of International Business and Economics

This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When the coefficients of the system and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. The authors also investigate the mean-field type optimal control problem for the system driven by mean-field type forward-backward stochastic differential equations(FBSDEs in short) with jumps, where the coefficients contain not only the state process but also its expectation under partially observed information. The maximum principle is established using convex variational technique. An example is given to illustrate the obtained results.

关键词： Forward-backward stochastic differential equation Girsanov's theorem jump diffusion Malliavin calculus maximum principle mean-field type partial information.

Distribution Approximation of Shrinkage Estimate in Censored Regression Model via Randomly Weighting Method

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Acta Mathematicae Applicatae Sinica 2019年第2期35卷 421-434页

作者： Xian-hui LIU Zhan-feng WANG Yao-hua WU department of Statistics and finance University of Science and Technology of China school of Statistics and research center of Applied Statistics Jiangxi University of Finance and Economics

Censored regression("Tobit") model is a special case of limited dependent variable regression model, and plays an important role in econometrics. Based on this model, all kinds of methods for variable or group variable selection have been developed and the corresponding shrinkage parameter estimates are widely studied. However, asymptotic distributions of the shrinkage estimates involve unknown nuisance parameters,such as density function of error term. To avoid estimating nuisance parameters, this paper presents a randomly weighting method to approximate to the asymptotic distribution of the shrinkage estimate. A computation procedure of random approximation is provided and asymptotic properties of the randomly weighting estimates are also obtained. The proposed methods are evaluated with extensively numerical studies and a women labor supply example.

关键词： Censored regression model variable selection asymptotic properties randomly weighting

Polynomial network autoregressive models with divergent orders

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Science China Mathematics 2023年第5期66卷 1073-1086页

作者： Bo Lei Wei Lan Nengsheng Fang Jing Zhou school of Statistics and center of Statistical research Southwestern University of Finance and EconomicsChengdu 611130China school of finance Southwestern University of Finance and EconomicsChengdu 611130China school of International Business Southwestern University of Finance and EconomicsChengdu 611130China

We propose a novel polynomial network autoregressive model by incorporating higher-order connected relationships to simultaneously model the effects of both direct and indirect connections. A quasimaximum likelihood estimation method is proposed to estimate the unknown influence parameters, and we demonstrate its consistency and asymptotic normality without imposing any distribution assumption. Moreover,an extended Bayesian information criterion is set for order selection with a divergent upper order. The application of the proposed polynomial network autoregressive model is demonstrated through both the simulation and the real data analysis.

关键词： diverging order extended Bayesian information criterion polynomial network autoregressive model quasi-maximum likelihood estimation