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101.
Simon P. Eveson Vladimir D. Stepanov Elena P. Ushakova 《Mathematische Nachrichten》2015,288(8-9):877-897
An embedding inequality of Sobolev type is characterized in the paper with help of a duality principle and boundedness criteria for the Hardy–Steklov integral operator in weighted Lebesgue spaces. 相似文献
102.
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. 相似文献
103.
In this work we focus on the efficient representation and computation of the eigenvalues and eigenfunctions of the surface Schrödinger operator that governs a class of nonlinear Ginzburg–Landau (GL) superconductivity models on rotationally symmetric Riemannian 2-manifolds S. We identify and analyze a complete orthonormal system in of eigenmodes having a variable-separated form. For the unknown functions in this ansatz, our analysis facilitates the identification of approximate spectral problems whose eigenvalues lie arbitrarily near corresponding eigenvalues of the Schrödinger operator. We then develop and implement an arbitrary order finite element method for the efficient numerical approximation of the eigenvalue problem. We also demonstrate our analysis, algorithm and its convergence rate using parallel computations performed on a variety of choices of smooth and non-smooth surfaces S. 相似文献
104.
Hyeonbae Kang Hyundae Lee Mikyoung Lim 《Mathematical Methods in the Applied Sciences》2015,38(9):1847-1854
We present a new systematic method to compute the Riemann mapping from the outside of the unit disc to the outside of a simply connected domain. We derive explicit relations between the coefficients of the Riemann mapping and the generalized polarization tensors associated with the domain. Because the generalized polarization tensors can be computed numerically, we are able to compute the coefficients of the Riemann mapping using these relations. Effectiveness of the method is validated by numerical examples. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
105.
Hironobu Sasaki 《偏微分方程通讯》2015,40(11):1959-2004
We study scattering problems for the one-dimensional nonlinear Dirac equation (?t + α?x + iβ)Φ = λ|Φ|p?1Φ. We prove that if p > 3 (resp. p > 3 + 1/6), then the wave operator (resp. the scattering operator) is well-defined on some 0-neighborhood of a weighted Sobolev space. In order to prove these results, we use linear operators D(t)xD(?t) and t?x + x?t ? α/2, where {D(t)}t∈? is the free Dirac evolution group. For the reader's convenience, in an appendix we list and prove fundamental properties of D(t)xD(?t) and t?x + x?t ? α/2. 相似文献
106.
107.
Tatiana Chernogorova Radoslav Valkov 《Numerical Methods for Partial Differential Equations》2015,31(3):822-846
We consider the locally one‐dimensional backward Euler splitting method to solve numerically the Hull and White problem for pricing European options with stochastic volatility in the presence of a mixed derivative term. We prove the first‐order convergence of the time‐splitting. The parabolic equation degenerates on the boundary x = 0 and we apply a fitted finite volume scheme to the equation to resolve the degeneracy and derive the fully discrete problem as we also investigate the discrete maximum principle. Numerical experiments illustrate the efficiency of our difference scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 822–846, 2015 相似文献
108.
有界平均振幅空间的研究在算子理论及全纯空间的研究中具有重要的作用.主要研究了有界平均振幅空间上乘法算子的性质,并且得到了托普里兹算子有界性及紧性的条件. 相似文献
109.
任颜波 《数学年刊A辑(中文版)》2015,36(2):119-128
对3类由凹函数生成的弱Orlicz鞅空间建立了相应的弱原子分解.作为应用,首先给出了这些弱Orlicz鞅空间上次线性算子有界的一个充分条件,并在此基础上证明了一些弱型鞅不等式,然后证明了关于这些弱Orlicz鞅空间的Marcinkiewicz型插值定理. 相似文献
110.