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Optimal Timing of Business Conversion for Solvency Improvement

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 744-757页

作者： Peng LI Ming ZHOU School of Finance Nanjing University of Finance and EconomicsNanjing 210023China Center for applied statistics and School of statistics Renmin University of ChinaBeijing 100872China

In this paper,we study the optimal timing to convert the risk of business for an insurance company in order to improve its *** cash flow of company evolves according to a jump-diffusion *** conversion option offers the company an opportunity to transfer the jump risk business *** exchange for this option,the company needs to pay both fixed and proportional transaction *** proportional cost can also be seen as the profit loading of the jump risk *** formulated this problem as an optimal stopping *** solving this stopping problem,we find that the optimal timing of business conversion mainly depends on the profit loading of the jump risk business.A larger profit loading would make the conversion option *** fixed cost,however,only delays the optimal timing of business *** the end,numerical results are provided to illustrate the impacts of transaction costs and environmental parameters to the optimal strategies.

关键词： optimal stopping jump-diffusion process conversion option

A STABILITY RESULT FOR TRANSLATINGSPACELIKE GRAPHS IN LORENTZ MANIFOLDS

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Acta Mathematica Scientia 2024年第2期44卷 474-483页

作者：高雅毛井吴传喜 Faculty of Mathematics and statistics Key Laboratory of Applied Mathematics of Hubei ProvinceHubei UniversityWuhan430062China

In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean *** prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.

关键词： mean curvature flow spacelike graphs translating spacelike graphs maximal spacelike graphs constant mean curvature Lorentz manifolds

Infinitely many dichotomous solutions for the Schrödinger-Poisson system

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Science China Mathematics 2024年第9期67卷 2049-2070页

作者： Yuke He Benniao Li Wei Long School of Mathematics and statistics and Jiangxi Provincial Center for applied Mathematics Jiangxi Normal UniversityNanchang 330022China

In this paper,we consider the following Schrodinger-Poisson system{-ε^(2)Δu+V(x)u+K(x)Φ(x)u=|u|^(p-1)u in R^(N),-ΔΦ(x)=K(x)u^(2)in RN,,where e is a small parameter,1 详细信息

In this paper,we consider the following Schrodinger-Poisson system{-ε^(2)Δu+V(x)u+K(x)Φ(x)u=|u|^(p-1)u in R^(N),-ΔΦ(x)=K(x)u^(2)in RN,,where e is a small parameter,1

关键词： dichotomous solutions non-degeneracy Schrodinger-Poisson system

Sparse-Grid Implementation of Fixed-Point Fast Sweeping WENO Schemes for Eikonal Equations

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Communications on applied Mathematics and Computation 2024年第1期6卷 3-29页

作者： Zachary M.Miksis Yong-Tao Zhang Department of applied and Computational Mathematics and statistics University of Notre DameNotre DameIN46556USA

Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping *** resulting iterative schemes have a fast convergence rate to steady-state ***,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local ***,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the *** multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational *** this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational ***,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)*** experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.

关键词： Fixed-point fast sweeping methods Weighted essentially non-oscillatory(WENO)schemes Sparse grids Static Hamilton-Jacobi(H-J)equations Eikonal equations

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

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Acta Mathematica Scientia 2024年第2期44卷 532-550页

作者：马文贤杨四辈 School of Mathematics and statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou730000China

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for *** precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/***,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

关键词： elliptic operator Kato square root problem Muckenhoupt weight Riesz transform reverse Hölder inequality

Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

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applied Mathematics and Mechanics(English Edition) 2024年第1期45卷 179-196页

作者： Yali ZHANG Yueting ZHOU Shenghu DING School of Mathematics and statistics Ningxia UniversityYinchuan 750021China School of Aerospace Engineering and applied Mechanics Tongji UniversityShanghai 200092China

Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical *** sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this *** simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert *** analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature *** contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi ***,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact *** on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact *** distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction ***,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads.

关键词： wavy surface periodic contact thermoelectric(TE)material Hilbert integral kernel

Fully Nonlinear Equations of Krylov Type on Riemannian Manifolds with Totally Geodesic Boundary

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1293-1307页

作者： Li CHEN Yan HE Faculty of Mathematics and statistics Hubei Key Laboratory of Applied MathematicsHubei UniversityWuhan 430000P.R.China

In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic *** prove the a priori estimates for solutions to these equations and ... 详细信息

关键词： The modified Schouten tensor k-convex Hessian type equation

First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1505-1520页

作者： Zhen YU Mao Zai TIAN Center for applied statistics School of StatisticsRenmin University of ChinaBeijing 100872P.R.China School of Mathematics and Data Science Changji UniversityChangji 831100P.R.China

The first passage time has many applications in fields like finance,econometrics,statistics,and ***,explicit formulas for the first passage density have only been obtained for a few *** paper derives an explicit formula for the first passage density of Brownian motion with twosided piecewise continuous boundaries which may have some points of *** are used to obtain a simplified formula for estimating the first passage ***,the results are also generalized to the case of two-sided general nonlinear *** can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density.

关键词： Boundary non-crossing probability first density passage density two-sided piecewise continuous boundaries Brownian motion

Empirical likelihood for spatial cross-sectional data models with matrix exponential spatial specification

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applied Mathematics(A Journal of Chinese Universities) 2024年第1期39卷 125-139页

作者： LIU Yan RONG Jian-rong QIN Yong-song Nanning University Nanning 530200China Center for applied Mathematics of Guangxi and College of Mathematics and statistics Guangxi Normal UniversityGuilin 541004China

In this paper,we study spatial cross-sectional data models in the form of matrix exponential spatial specification(MESS),where MESS appears in both dependent and error *** empirical likelihood(EL)ratio statistics are established for the parameters of the MESS *** is shown that the limiting distributions of EL ratio statistics follow chi-square distributions,which are used to construct the confidence regions of model *** experiments are conducted to compare the performances of confidence regions based on EL method and normal approximation method.

关键词： MESS empirical likelihood con dence region