ISSN 0253-2778

CN 34-1054/N

2019 Vol. 49, No. 8

Display Method:
Large induced subgraph with restricted degrees in trees
HUANG Ziyang, HOU Xinmin
2019, 49(8): 603-605. doi: 10.3969/j.issn.0253-2778.2019.08.001
A problem was proposed to determine for a tree T the size of the largest SV(T) such that all vertices in T[S] have either degree 1 or degree 0 (mod k). Here it was proved that, for integer k≥2, every tree T contains an induced subgraph of order at least ck|V(T)| with all degrees either equal to 1 or 0 (mod k), where ck=3/4 when k=2, and ck=2/3 when k≥3. Moreover, the bounds are best possible. This gives a good answer to the problem.
Berry-Esséen type bound of sample quantiles for positively associated sequence
HU Xueping, ZHANG Tong, GUO Zhidong, ZHANG Heng
2019, 49(8): 606-613. doi: 10.3969/j.issn.0253-2778.2019.08.002
By utilizing some inequalities for positively associated (PA) random variables, a Berry-Esséen type bound of sample quantiles for PA samples under mild conditions was studied. The rate of uniform asymptotic normality was presented and the rate of convergence is near O(n-1/6) when the third moment is finite.
The computing formula for generalized Euler functions
LIAO Qunying
2019, 49(8): 614-619. doi: 10.3969/j.issn.0253-2778.2019.08.003
Let n and e be positive integers. Based on elementary methods and techniques, the explicit formula for φe(n)(e=pr, ∏ti=1qi) was given for the case q1≡…≡qt≡1(mod p) or q1≡…≡qt≡-1(mod p), where p,q1,…,qt are distinct primes, t and r are both positive integers, thus generalizing the previous results.
The shock wave solution to nonlinear nonlocal singularly perturbed fractional order equation Cauchy problem
XU Jianzhong, WANG Weigang, MO Jiaqi
2019, 49(8): 620-624. doi: 10.3969/j.issn.0253-2778.2019.08.004
A class of Cauchy problem for the nonlinear nonlocal singular perturbation fractional order equation was considered. First, the outer solution to the original Cauchy problem was obtained. Then, using the stretched variables and the composing expansion method the shock wave layer and initial layer were constructed. Finally, using the theory of differential inequality the asymptotic behavior of the solution to the original Cauchy problem of nonlinear nonlocal singular perturbation fractional order equation was studied and its uniformly valid asymptotic estimation was proved.
Asymptopic solution to nonlinear generalized fractional order thermal wave equation
CHEN Huaijun, MO Jiaqi, XU Jianzhong
2019, 49(8): 625-629. doi: 10.3969/j.issn.0253-2778.2019.08.005
A class of nonlinear generalized thermal wave equation was considered .Firstly, the solution to reduced thermal wave equation was obtained.Next, the arbitrary order asymptopic solutions to generalized nonlinear disturbed thermal wave equation initial-boundary value problem were constructed by using the method of functional analysis homotopic mapping.An example was given and the accuracy of its asymptopic solution was obtained.Finally, the physical sense of the solution was briefly stated. The approximate analysis solution makes up for the simple numerical simulation solution deficiency.
The Bayes estimation of parameters of spatial autoregressive model
WU Shipeng, ZHANG Huiguo, WANG Heling
2019, 49(8): 630-634. doi: 10.3969/j.issn.0253-2778.2019.08.006
First, the linear Bayes was used to estimate the parameters of spatial autoregressive model, and the superiorities of the linear Bayes estimator over two-step least square estimator were studied in terms of the mean square error matrix (MSEM) criterion. Then, the estimation of spatial autocorrelation coefficient was implemented by Metropolis algorithm. Finally, the superiority of the linear Bayes estimation and two-step least square estimation was compared by simulation experiments.
VaR estimation based on quantile regression forest and risk factors analysis
GOU Xiaoju, WANG Qian
2019, 49(8): 635-644. doi: 10.3969/j.issn.0253-2778.2019.08.007
Quantile regression forests as a nonparametric and ensemble method were built to estimate the VaR of Shanghai Composite Index and the S&P 500 Index at different confidence levels. Meanwhile,other methods were built for comparison, including historic simulation,GARCH, elastic net,threshold quantile regression model and CAViaR, and the superiority of the proposed method was verified. Further, a new measurement method of variable importance based on the quantile regression forest was defined to judge the importance of various factors on the risk value, and it was discovered that the past one day yield has the greatest influence on the risk value of the Shanghai Composite Index, and that the volatility has the greatest influence on S&P 500 Index risk value. At the same time, the risk conduction between China and US is weak. Further, by dynamically analyzing the partial dependence between the factors and risk value, the “black box” problem of machine learning used in financial applications has been remedied to some extent.
The influence of Internet finance on the innovation ability of commercial banks in the new situation
YAN Juntao, BI Xiuchun, ZHANG Shuguang
2019, 49(8): 645-654. doi: 10.3969/j.issn.0253-2778.2019.08.008
The rapid development of Internet finance has caused an indisputable impact on the banking industry. The best way for banks to respond to the impact of the Internet finance is self-innovation. Internet finance has both the negative impact of the squeezing effect (competition effect) and the positive impact of the forcing effect (technology spillover effect) on commercial banks’ innovation. The study of the relationship between the two and the results of their joint actions are significant for the development of banks’ innovation in the Internet financial environment. Here the second term of the agent variable of Internet finance was introduced to build a nonlinear model to study the impact of Internet finance on banks’ innovation ability from three aspects: large-scale state-owned banks, joint-stock banks, and city commercial banks. The empirical study used the data from 2011 to 2017, employing both static and dynamic panel data methods. It was found that the impact of Internet finance on the index of bank innovation ability-the non-interest income ratio-has a U-shaped or inverted U-shaped trend relationship in time series, and that the trend relationship between Internet finance and the proportion of non-interest income of different banks is different. Therefore, different types of banks should combine their own backgrounds and advantages to innovate, enhance their own innovation capabilities and intermediate business profitability, and optimize their own service channels and models to cope with the impact of Internet finance.
Optimal dynamic cointegrated pairs trading strategies with state-dependent risk aversion
DENG Xinning, BI Xiuchun, ZHANG Shuguang
2019, 49(8): 655-667. doi: 10.3969/j.issn.0253-2778.2019.08.009
Cointegrated pairs trading attempts to make profits when cointegrated assets depart from their equilibrium. For the mean-variance model with constant risk aversion, the optimal dynamic cointegrated pairs trading strategy shows that the allocation amounts on risky assets depend only on time but not on wealth, which goes against common sense.The optimal allocation of cointegration assets under the mean-variance model with state-dependent risk aversion was studied, and an algebraic form of the optimal strategy was obtained by solving an extended HJB equation. The strategy shows that the optimal allocation amounts depend not only on time but also on current wealth, and the strategy makes sure that the total assets remain positive all the time. Thus our strategy is more economically reasonable compared to those under constant risk aversion. The numerical example implies that our strategy behaves more steadily in terms of asset allocation, and there is an increasing trend in the allocation amounts as time goes by, a in contrast to the strategy under constant risk aversion. In addition, the influence of cointegration coefficients matrix and mean-reverting speed on the strategy was studied and explained.
Dynamic correlation of quantile regression model based on smooth transition mechanism
YE Wuyi, MA Ronggui, WU Zun
2019, 49(8): 668-679. doi: 10.3969/j.issn.0253-2778.2019.08.010
A quantile regression model was built under the smooth transition mechanism with the market volatility index (VIX) as smooth transition variable to study the non-linear effects of the US stock market on most of the global stock markets. The transition position of the smoothing mechanism model can describe the sensitive point of global stock market to the US stock market, and the transition slope describes the conversion rate of interconnectedness. The empirical results show that there does exist nonlinear mechanism transformation in the correlation of international stock markets, and that almost all global stock markets are subject to the impact of the US stock market. Moreover, under different quantiles, the conversion rates between different mechanism are not identical. Evident difference is found under low quantiles, which suggests that the correlation between financial markets is mainly due to tail-risk conduction. Then the collected data was divided into three sub samples and were studied respectively using the proposed model. The results show that there is a significant difference between position parameters during and after the crisis. During the crisis the position parameters decreased, and the correlation improved significantly under low quantiles,indicating that the proposed model is feasible to study the dynamic correlation between financial markets and that the exogenous variable VIX has a considerable influence on the correlation between financial markets. This provides a new perspective for international investors and policy makers to consider the impact of the US economy on global equity markets with the help of the VIX.
Decision of enterprises’ product differentiation and pricing with heterogeneous consumers
TANG Weijun
2019, 49(8): 680-688. doi: 10.3969/j.issn.0253-2778.2019.08.011
After making reasonable assumptions of switch costs and product costs ,based on the Hotelling’s model, the Mussa and Rosen’s model, enterprises’ product and pricing strategies in the competitive environment were discussed, and the influences of consumers’ heterogeneities and product costs on enterprises’ strategies were analyzed. Research shows that if two enterprises implement single pricing or discriminatory pricing, they will follow the principle of minimum differentiation, and that if they implement different pricing strategies, the one that adopts discriminatory pricing will obtain higher equilibrium quality, and its profits will be also improved .At the same time, the more sensitive consumers are to quality, or the more quality-sensitive people are, the higher the equilibrium qualities and prices will rise, and the more enterprises’ profits will decrease. The more sensitive consumers are to price, or the more price-sensitive people are, the more equilibrium qualities and prices will decrease. With the increases of cost coefficients, the equilibrium qualities will lower, and when the marginal cost coefficients are greater than a certain value, enterprises will be driven out of the market. Finally, an example was analyzed, and was concluded that enterprises’ optimal strategies are to implement discrimination pricing.