Asymptotic Stability of Equilibrium State to the Mixed Initial-Boundary Value Problem for Quasilinear Hyperbolic Systems

Under the internal dissipative condition, the Cauchy problem for inhomogeneous quasilinear hyperbolic systems with small initial data admits a unique global C1 solution, which exponentially decays to zero as t → +∞, while if the coefficient matrixΘ of boundary conditions satisfies the boundary dissipative condition, the mixed initialboundary value problem with small initial data for quasilinear hyperbolic systems with nonlinear terms of at least second order admits a unique global C1 solution, which also exponentially decays to zero as t → +∞. In this paper, under more general conditions, the authors investigate the combined effect of the internal dissipative condition and the boundary dissipative condition, and prove the global existence and exponential decay of the C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with small initial data. This stability result is applied to a kind of models, and an example is given to show the possible exponential instability if the corresponding conditions are not satisfied.     

On the stability of two new two-step explicit methods for the numerical integration of second order initial value problem on a variable mesh

We present two novel two-step explicit methods for the numerical solution of the second order initial value problem on a variable mesh. In the case of a constant mesh the method is superstable in the sense of Chawla (1985). Numerical experimentation is provided to verify the stability analysis.     

一类n-阶m-点奇异边值问题的正解

研究n-阶m-点奇异边值问题其中h(t)允许在t=0,t=1处奇异,f(t,v_0,v_1,…,v_(n-2))允许在v_i=0(i=0,1,…,n-2)处奇异.利用锥拉伸与压缩不动点定理得到了上述奇异边值问题正解的存在性.     

Multiplicity of positive solutions to period boundary value problems for second order impulsive differential equations

This paper deals with the existence and multiplicity of positive solutions to second order period boundary value problems with impulse effects. The proof of our main results relies on a well-known fixed point theorem in cones. The paper extends some previous results and reports some new results about impulsive differential equations.     

关于曲线积分中值定理“中间点”渐近性的进一步结果

给出一个曲线积分学中值定理及其"中间点"渐近性分析,其结果还概括了近五年来关于积分学第一中值定理"中间点"渐近性的众多结果.     

On the order of summability of the Fourier inversion formula

In this article we show that the order of the point value, in the sense of Łojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesàro summable to the distributional point value of order k+1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesàro summable of order k, then the distribution is the (k+1)-th derivative of a locally integrable function, and the distribution has a distributional point value of order k+2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems.     

Evaluation and default time for companies with uncertain cash flows

In this study, we propose a modelling framework for evaluating companies financed by random liabilities, such as insurance companies or commercial banks. In this approach, earnings and costs are driven by double exponential jump–diffusion processes and bankruptcy is declared when the income falls below a default threshold, which is proportional to the charges. A change of numeraire, under the Esscher risk neutral measure, is used to reduce the dimension. A closed form expression for the value of equity is obtained in terms of the expected present value operators, with and without disinvestment delay. In both cases, we determine the default threshold that maximizes the shareholder’s equity. Subsequently, the probabilities of default are obtained by inverting the Laplace transform of the bankruptcy time. In numerical applications of the proposed model, we apply a procedure for calibration based on market and accounting data to explain the behaviour of shares for two real-world examples of insurance companies.     

基于Copula-EVT模型的我国股票市场流动性调整的VaR和ES研究

结合相依结构函数Copula和极值理论EVT,构建了我国股票市场经流动性调整的La-Copula-EVT风险价值模型,并用沪深收益序列的分笔高频数据进行了实证分析,发现我国沪深股市收益序列的上尾和下尾都存在较高相关性,后验测试结果表明构建的模型能够对实际损失进行很好的拟合;然后在该模型的基础上进一步分析了我国沪深股市的风险价值和预期不足在不同置信区间的敏感度差异,确定了适合La-Copula-EVT模型的最优置信度区间。