Pricing Variance Swaps in a Hybrid Model of Stochastic Volatility and Interest Rate with Regime-Switching

In this paper, we consider the problem of pricing discretely-sampled variance swaps based on a hybrid model of stochastic volatility and stochastic interest rate with regime-switching. Our modeling framework extends the Heston stochastic volatility model by including the Cox-Ingersoll-Ross (CIR) stochastic interest rate model. In addition, certain model parameters in our model switch according to a continuous-time observable Markov chain process. This enables our model to capture several macroeconomic issues such as alternating business cycles. A semi-closed form pricing formula for variance swaps is derived. The pricing formula is assessed through numerical implementation, where we validate our pricing formula against the Monte Carlo simulation. The impact of incorporating regime-switching for pricing variance swaps is also discussed, where variance swaps prices with and without regime-switching effects are examined in our model. We also explore the economic consequence for the prices of variance swaps by allowing the Heston-CIR model to switch across three different regimes.     

A note on blow-up of solution for a class of semilinear pseudo-parabolic equations

In this short note, we revisit the blow-up of solution for the initial boundary value problem of semilinear pseudo-parabolic equations with low/critical initial energy stated in Xu and Su (2013) [4], and amend the proofs of the original paper.     

一种薄板弯曲问题的四边形位移单元

本文基于修正势能泛函,引入广义协调的概念,导出了一种具有12个自由度的薄板弯曲四边形位移单元LGC—Q12,这种单元协调性好,列式简单,计算精度高。并且能近似地通过分片检验。     

Bending problems of rectangular Reissner plate with free edges laid on tensionless Winkler foundations

In this paper,an analytical method for solving the bending problems of rectangularReissner plate with free edges under arbitrary loads laid on tensionless Winkler foundationsis proposed.By assuming proper form of Fourier series with supplementary terms,whichmeet derivable conditions,for deflection and shear force functions,the basic differentialequations with given boundary conditions can be transformed into a set of simple infinitealgebraic equations.For common Winkler foundations,this set of equations can be solveddirectly and for tensionless Winkler foundations,it is a set of weak nonlinear algebraicequations,the solution of which can be obtained easily by using iterative procedures.     

An inequality concerning the growth bound of an evolution family and the norm of a convolution operator

Let \(\mathcal {U}=\{U(t,s)\}_{t\ge s\ge 0}\) be a strongly continuous and exponentially bounded evolution family acting on a complex Banach space X and let \(\mathcal {X}\) be a certain Banach function space of X-valued functions. We prove that the growth bound of the family \(\mathcal {U}\) is less than or equal to \(-\frac{1}{c(\mathcal {U}, \mathcal {X})}\) provided that the convolution operator \(f\mapsto \mathcal {U}*f\) acts on \(\mathcal {X}.\) It is well known that under the latter assumption, the convolution operator is bounded and then \(c(\mathcal {U}, \mathcal {X})\) denotes (ad-hoc) its norm in \(\mathcal {L}(\mathcal {X}).\) As a consequence, we prove that if \(\sup \nolimits _{s\ge 0}\int \nolimits _{s}^\infty \Vert U(t,s)\Vert dt=u_1(\mathcal {U})<\infty ,\) then \(\omega _0(\mathcal {U})u_1(\mathcal {U})\le -1.\) Finally, we give an example showing that the accuracy of the estimates may be quite accurate.     

非Lipschitz的渐近弱伪压缩映象不动点的迭代逼近

给出了渐近弱伪压缩映象概念,在Banach空间中讨论不动点的迭代逼近问题,所得结果改进和推广了已有的一些结果。     

小长径比弹丸加装大展弦比尾翼的气动特性研究

为了提高小长径比弹丸射击质量,设计了一种大展弦比张开式尾翼,采用AUSM+格式、SST(shearstress transport)湍流模型和隐式算法(lower-upper symmetric Gauss-Seidel implicit method, LU-SGS),求解三维RANS 方程,对前体形状完全相同,不同展弦比的3 种尾翼弹进行了数值模拟,得到了三者在马赫数1.5~3.5 下的气动力特性的差异,分析其原因,并给出了不同展弦比张开式尾翼的适用范围. 计算结果表明:C型弹的升阻比较B 型弹在1.5 马赫数区域附近增加了7% 以上,当马赫数达到2.5 以上时,A 型弹的升阻比大于B 型弹和C 型弹,在3.5 马赫数区域附近A 型弹的升阻比较B 型弹增加了5.4% 以上. 3 种弹丸的俯仰力矩系数随着马赫数的增大而负向减少,且减少的趋势随着展弦比的增加而增大. A 型弹、B 型弹、C 型弹的静稳定裕度的变化范围分别为4%~20.3%,8.5%~23.2%,11.4%~25.6%.     

Krasnoselskii‐type fixed point theorems with applications to Hammerstein integral equations in spaces

In this paper, we study fixed point theorems and new variants of some nonlinear altenatives of Krasnoselskii type in Banach spaces by using measures of weak noncompactness. Then we give an application to solve a nonlinear Hammerstein integral equation in L¹ spaces.     

The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption

In this paper we prove some new equivalences between convergence of the Ishikawa and Mann iteration sequences with errors in two schemes by Xu [Y.G. Xu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998) 91-101] and Liu [L.S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995) 114-125], respectively, for strongly successively pseudocontractive mappings. Our main results improve and extend the corresponding results of the all references listed in this article.     

光场显微镜实现裸眼三维实时显示

提出了一种将光场显微镜与裸眼三维显示技术相结合的方法,实现了利用光场显微镜对微观样品进行三维裸眼实时观察的技术。该技术将光场显微镜得到的子图像阵列直接投影在微透镜阵列的焦平面上,在空间一定区域内双眼可分别观看到两幅不同视角图像,使观察者产生立体视觉。该系统具有结构简单,无需相干光源,无需佩戴特殊眼镜,可多人同时观看等优点,应用前景广泛。