In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the...In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the reset option with a single reset date and the phenomena of delta of the reset jumps existing in the reset option during the reset date are discussed. The closed-form formulae of pricing for two kinds of power options are derived in the end.展开更多
In this paper,a second-order fnite-diference scheme is investigated for time-dependent space fractional difusion equations with variable coefcients.In the presented scheme,the Crank-Nicolson temporal discretization an...In this paper,a second-order fnite-diference scheme is investigated for time-dependent space fractional difusion equations with variable coefcients.In the presented scheme,the Crank-Nicolson temporal discretization and a second-order weighted-and-shifted Grünwald-Letnikov spatial discretization are employed.Theoretically,the unconditional stability and the second-order convergence in time and space of the proposed scheme are established under some conditions on the variable coefcients.Moreover,a Toeplitz preconditioner is proposed for linear systems arising from the proposed scheme.The condition number of the preconditioned matrix is proven to be bounded by a constant independent of the discretization step-sizes,so that the Krylov subspace solver for the preconditioned linear systems converges linearly.Numerical results are reported to show the convergence rate and the efciency of the proposed scheme.展开更多
This paper considers a discrete-time queue with N-policy and LAS-DA(late arrival system with delayed access) discipline.By using renewal process theory and probability decomposition techniques,the authors derive the r...This paper considers a discrete-time queue with N-policy and LAS-DA(late arrival system with delayed access) discipline.By using renewal process theory and probability decomposition techniques,the authors derive the recursive expressions of the queue-length distributions at epochs n^-,n^+,and n.Furthermore,the authors obtain the stochastic decomposition of the queue length and the relations between the equilibrium distributions of the queue length at different epochs(n^-,n^+,n and departure epoch D_n).展开更多
A moving collocation method is proposed and implemented to solve time fractional differential equations.The method is derived by writing the fractional differential equation into a form of time difference equation.The...A moving collocation method is proposed and implemented to solve time fractional differential equations.The method is derived by writing the fractional differential equation into a form of time difference equation.The method is stable and has a third-order convergence in space and first-order convergence in time for either linear or nonlinear equations.In addition,the method is used to simulate the blowup in the nonlinear equations.展开更多
This paper establishes a lattice Boltzmann method （LBM） with two amending functions for solving partial differential equations （PDEs） arising in Asian and lookback options pricing. The time evolution of stock pric...This paper establishes a lattice Boltzmann method （LBM） with two amending functions for solving partial differential equations （PDEs） arising in Asian and lookback options pricing. The time evolution of stock prices can be regarded as the movement of randomizing particles in different directions, and the discrete scheme of LBM can be interpreted as the binomial models. With the Chapman-Enskog multi-scale expansion, the PDEs are recovered correctly from the continuous Boltzmann equation and the computational complexity is O（N）, where N is the number of space nodes. Compared to the traditional LBM, the coefficients of equilibrium distribution and amending functions are taken as polynomials instead of constants. The stability of LBM is studied via numerical examples and numerical comparisons show that the LBM is as accurate as the existing numerical methods for pricing the exotic options and takes much less CPU time.展开更多
In this paper, high-order numerical analysis of finite element method（FEM） is presented for twodimensional multi-term time-fractional diffusion-wave equation（TFDWE）. First of all, a fully-discrete approximate sche...In this paper, high-order numerical analysis of finite element method（FEM） is presented for twodimensional multi-term time-fractional diffusion-wave equation（TFDWE）. First of all, a fully-discrete approximate scheme for multi-term TFDWE is established, which is based on bilinear FEM in spatial direction and Crank-Nicolson approximation in temporal direction, respectively. Then the proposed scheme is proved to be unconditionally stable and convergent. And then, rigorous proofs are given here for superclose properties in H-1-norm and temporal convergence in L-2-norm with order O（h-2＋ τ-（3-α））, where h and τ are the spatial size and time step, respectively. At the same time, theoretical analysis of global superconvergence in H-1-norm is derived by interpolation postprocessing technique. At last, numerical example is provided to demonstrate the theoretical analysis.展开更多
This paper develops a fast Laplace transform method for solving the complex PDE system arising from Parisian and Parasian option pricing.The value functions of the options are governed by a system of partial different...This paper develops a fast Laplace transform method for solving the complex PDE system arising from Parisian and Parasian option pricing.The value functions of the options are governed by a system of partial differential equations(PDEs)of two and three dimensions.Applying the Laplace transform to the PDEs with respect to the calendar time to maturity leads to a coupled system consisting of an ordinary differential equation(ODE)and a 2-dimensional partial differential equation(2d-PDE).The solution to this ODE is found analytically on a specific parabola contour that is used in the fast Laplace inversion,whereas the solution to the 2d-PDE is approximated by solving 1-dimensional integro-differential equations.The Laplace inversion is realized by the fast contour integral methods.Numerical results confirm that the Laplace transform methods have the exponential convergence rates and are more efficient than the implicit finite difference methods,Monte Carlo methods and moving window methods.展开更多
In this paper,we construct tight lower and upper bounds for the price of an American strangle,which is a special type of strangle consisting of long positions in an American put and an American call,where the early ex...In this paper,we construct tight lower and upper bounds for the price of an American strangle,which is a special type of strangle consisting of long positions in an American put and an American call,where the early exercise of one side of the position will knock out the remaining side.This contract was studied in Chiarella and Ziogas(J Econ Dyn Control 29:31–62,2005)with the corresponding nonlinear integral equations derived,which are hard to be solved efficiently through numerical methods.We extend the approach in the paper of Broadie and Detemple(Rev Finance Stud 9:1211–1250,1996)from the case of American call options to the case of American strangles.We establish theoretical properties of the lower and upper bounds,and propose a sequential optimization algorithm in approximating the early exercise boundary of the American strangle. The theoretical bounds obtained can beeasily evaluated, and numerical examples confirm the accuracy of the approximationscompared to the literature.展开更多
This paper studies a system of semi-linear fractional diffusion equations which arise in competitive predator-preymodels by replacing the second-order derivatives in the spatial variables with fractional derivatives o...This paper studies a system of semi-linear fractional diffusion equations which arise in competitive predator-preymodels by replacing the second-order derivatives in the spatial variables with fractional derivatives of order less than two.Moving finite element methods are proposed to solve the system of fractional diffusion equations and the convergence rates of the methods are proved.Numerical examples are carried out to confirm the theoretical findings.Some applications in anomalous diffusive Lotka-Volterra and Michaelis-Menten-Holling predator-preymodels are studied.展开更多
Using recursive method, this paper studies the queue size properties at any epoch n＋ in Geom/G/ I（E, SV） queueing model with feedback under LASDA （late arrival system with delayed access） setup. Some new results ...Using recursive method, this paper studies the queue size properties at any epoch n＋ in Geom/G/ I（E, SV） queueing model with feedback under LASDA （late arrival system with delayed access） setup. Some new results about the recursive expressions of queue size distribution at different epoch （n＋, n, n-） are obtained. Furthermore the important relations between stationary queue size distribution at different epochs are discovered. The results are different from the relations given in M/G/1 queueing system. The model discussed in this paper can be widely applied in many kinds of communications and computer network.展开更多
With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equatio...With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations （FPDEs）. The unconditional stability and convergence rates of 2 -a for time and r for space are proved when the method is used for the linear time FPDEs with a-th order time derivatives. Numerical exam-ples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method.展开更多
This paper develops and analyzes a moving mesh finite difference method for solving partial integro-differential equations. First, the time-dependent mapping of the coordinate transformation is approximated by a a pie...This paper develops and analyzes a moving mesh finite difference method for solving partial integro-differential equations. First, the time-dependent mapping of the coordinate transformation is approximated by a a piecewise linear function in time. Then, piecewise quadratic polynomial in space and an efficient method to discretize the memory term of the equation is designed using the moving mesh approach. In each time slice, a simple piecewise constant approximation of the integrand is used, and thus a quadrature is constructed for the memory term. The central finite difference scheme for space and the backward Euler scheme for time are used. The paper proves that the accumulation of the quadrature error is uniformly bounded and that the convergence of the method is second order in space and first order in time. Numerical experiments are carried out to confirm the theoretical predictions.展开更多
Let G be a bounded open subset in the complex plane and let H 2(G)denote the Hardy space on G.We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Rieman...Let G be a bounded open subset in the complex plane and let H 2(G)denote the Hardy space on G.We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1–1 with respect to the Lebesgue measure on?D and if the Riemann map belongs to the weak-star closure of the polynomials in H∞(W).Our main theorem states:in order that for each M∈Lat(M z),there exist u∈H∞(G)such that M=∨{uνH 2(G)},it is necessary and sufficient that the following hold:each component of G is a perfectly connected domain the harmonic measures of the components of G are mutually singular the set of polynomials is weak-star dense in H∞(G).Moreover,if G satisfies these conditions,then every M∈Lat(M z)is of the form uH 2(G),where u∈H∞(G)and the restriction of u to each of the components of G is either an inner function or zero.展开更多
This paper deals with the global strong solution to the three-dimensional(3D)full compressible Navier-Stokes systems with vacuum. The authors provide a sufficient condition which requires that the Sobolev norm of the ...This paper deals with the global strong solution to the three-dimensional(3D)full compressible Navier-Stokes systems with vacuum. The authors provide a sufficient condition which requires that the Sobolev norm of the temperature and some norm of the divergence of the velocity are bounded, for the global regularity of strong solution to the 3D compressible Navier-Stokes equations. This result indicates that the divergence of velocity fields plays a dominant role in the blowup mechanism for the full compressible Navier-Stokes equations in three dimensions.展开更多
The best breakdown point robustness is one of the most outstanding features of the univariate median.For this robustness property,the median,however,has to pay the price of a low effciency at normal and other light-ta...The best breakdown point robustness is one of the most outstanding features of the univariate median.For this robustness property,the median,however,has to pay the price of a low effciency at normal and other light-tailed models.Affine equivariant multivariate analogues of the univariate median with high breakdown points were constructed in the past two decades.For the high breakdown robustness,most of them also have to sacrifice their effciency at normal and other models,nevertheless.The affine equivariant maximum depth estimator proposed and studied in this paper turns out to be an exception.Like the univariate median,it also possesses a highest breakdown point among all its multivariate competitors.Unlike the univariate median,it is also highly efficient relative to the sample mean at normal and various other distributions,overcoming the vital low-effciency shortcoming of the univariate and other multivariate generalized medians.The paper also studies the asymptotics of the estimator and establishes its limit distribution without symmetry and other strong assumptions that are typically imposed on the underlying distribution.展开更多
In this paper,a two dimensional(2D)fractional Black-Scholes(FBS)model on two assets following independent geometric Lévy processes is solved numerically.A high order convergent implicit difference scheme is const...In this paper,a two dimensional(2D)fractional Black-Scholes(FBS)model on two assets following independent geometric Lévy processes is solved numerically.A high order convergent implicit difference scheme is constructed and detailed numerical analysis is established.The fractional derivative is a quasidifferential operator,whose nonlocal nature yields a dense lower Hessenberg block coefficient matrix.In order to speed up calculation and save storage space,a fast bi-conjugate gradient stabilized(FBi-CGSTAB)method is proposed to solve the resultant linear system.Finally,one example with a known exact solution is provided to assess the effectiveness and efficiency of the presented fast numerical technique.The pricing of a European Call-on-Min option is showed in the other example,in which the influence of fractional derivative order and volatility on the 2D FBS model is revealed by comparing with the classical 2D B-S model.展开更多
文摘In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the reset option with a single reset date and the phenomena of delta of the reset jumps existing in the reset option during the reset date are discussed. The closed-form formulae of pricing for two kinds of power options are derived in the end.
基金This research was supported by research Grants,12306616,12200317,12300519,12300218 from HKRGC GRF,11801479 from NSFC,MYRG2018-00015-FST from University of Macao,and 0118/2018/A3 from FDCT of Macao,Macao Science and Technology Development Fund 0005/2019/A,050/2017/Athe Grant MYRG2017-00098-FST and MYRG2018-00047-FST from University of Macao.S。
文摘In this paper,a second-order fnite-diference scheme is investigated for time-dependent space fractional difusion equations with variable coefcients.In the presented scheme,the Crank-Nicolson temporal discretization and a second-order weighted-and-shifted Grünwald-Letnikov spatial discretization are employed.Theoretically,the unconditional stability and the second-order convergence in time and space of the proposed scheme are established under some conditions on the variable coefcients.Moreover,a Toeplitz preconditioner is proposed for linear systems arising from the proposed scheme.The condition number of the preconditioned matrix is proven to be bounded by a constant independent of the discretization step-sizes,so that the Krylov subspace solver for the preconditioned linear systems converges linearly.Numerical results are reported to show the convergence rate and the efciency of the proposed scheme.
基金supported by the National Natural Science Foundation of China under Grant No.70871084The Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 200806360001a grant from the "project 211(PhaseⅢ)" of the Southwestern University of Finance and Economics, Scientific Research Fund of Southwestern University of Finance and Economics
文摘This paper considers a discrete-time queue with N-policy and LAS-DA(late arrival system with delayed access) discipline.By using renewal process theory and probability decomposition techniques,the authors derive the recursive expressions of the queue-length distributions at epochs n^-,n^+,and n.Furthermore,the authors obtain the stochastic decomposition of the queue length and the relations between the equilibrium distributions of the queue length at different epochs(n^-,n^+,n and departure epoch D_n).
基金supported by National Natural Science Foundation of China(Grant No.10901027)
文摘A moving collocation method is proposed and implemented to solve time fractional differential equations.The method is derived by writing the fractional differential equation into a form of time difference equation.The method is stable and has a third-order convergence in space and first-order convergence in time for either linear or nonlinear equations.In addition,the method is used to simulate the blowup in the nonlinear equations.
基金The authors were grateful to the anonymous referees for their valuable suggestions that led to a greatly improved paper. This work was supported by the National Natural Science Foundation of China （Grant No. 11171274） and the Program for New Century Excellent Talents in University （Grant No. NCET-12-0922）.
文摘This paper establishes a lattice Boltzmann method （LBM） with two amending functions for solving partial differential equations （PDEs） arising in Asian and lookback options pricing. The time evolution of stock prices can be regarded as the movement of randomizing particles in different directions, and the discrete scheme of LBM can be interpreted as the binomial models. With the Chapman-Enskog multi-scale expansion, the PDEs are recovered correctly from the continuous Boltzmann equation and the computational complexity is O（N）, where N is the number of space nodes. Compared to the traditional LBM, the coefficients of equilibrium distribution and amending functions are taken as polynomials instead of constants. The stability of LBM is studied via numerical examples and numerical comparisons show that the LBM is as accurate as the existing numerical methods for pricing the exotic options and takes much less CPU time.
基金Supported by the National Natural Science Foundation of China(Nos.11771438,11471296)the Key Scientific Research Projects in Universities of Henan Province(No.19B110013)the Program for Scientific and Technological Innovation Talents in Universities of Henan Province(No.19HASTIT025)
文摘In this paper, high-order numerical analysis of finite element method（FEM） is presented for twodimensional multi-term time-fractional diffusion-wave equation（TFDWE）. First of all, a fully-discrete approximate scheme for multi-term TFDWE is established, which is based on bilinear FEM in spatial direction and Crank-Nicolson approximation in temporal direction, respectively. Then the proposed scheme is proved to be unconditionally stable and convergent. And then, rigorous proofs are given here for superclose properties in H-1-norm and temporal convergence in L-2-norm with order O（h-2＋ τ-（3-α））, where h and τ are the spatial size and time step, respectively. At the same time, theoretical analysis of global superconvergence in H-1-norm is derived by interpolation postprocessing technique. At last, numerical example is provided to demonstrate the theoretical analysis.
基金supported by National Natural Science Foundation of China(Grant No.11671323)Program for New Century Excellent Talents in University of China(Grant No.NCET-12-0922)+1 种基金the Fundamental Research Funds for the Central Universities of China(Grant No.JBK1805001)Hunan Province Science Foundation of China(Grant No.2020JJ4562)。
文摘This paper develops a fast Laplace transform method for solving the complex PDE system arising from Parisian and Parasian option pricing.The value functions of the options are governed by a system of partial differential equations(PDEs)of two and three dimensions.Applying the Laplace transform to the PDEs with respect to the calendar time to maturity leads to a coupled system consisting of an ordinary differential equation(ODE)and a 2-dimensional partial differential equation(2d-PDE).The solution to this ODE is found analytically on a specific parabola contour that is used in the fast Laplace inversion,whereas the solution to the 2d-PDE is approximated by solving 1-dimensional integro-differential equations.The Laplace inversion is realized by the fast contour integral methods.Numerical results confirm that the Laplace transform methods have the exponential convergence rates and are more efficient than the implicit finite difference methods,Monte Carlo methods and moving window methods.
基金The work was supported by the National Natural Science Foundation of China(No.11671323)Program for New Century Excellent Talents in University(No.NCET-12-0922)the Fundamental Research Funds for the Central Universities(No.15CX141110).
文摘In this paper,we construct tight lower and upper bounds for the price of an American strangle,which is a special type of strangle consisting of long positions in an American put and an American call,where the early exercise of one side of the position will knock out the remaining side.This contract was studied in Chiarella and Ziogas(J Econ Dyn Control 29:31–62,2005)with the corresponding nonlinear integral equations derived,which are hard to be solved efficiently through numerical methods.We extend the approach in the paper of Broadie and Detemple(Rev Finance Stud 9:1211–1250,1996)from the case of American call options to the case of American strangles.We establish theoretical properties of the lower and upper bounds,and propose a sequential optimization algorithm in approximating the early exercise boundary of the American strangle. The theoretical bounds obtained can beeasily evaluated, and numerical examples confirm the accuracy of the approximationscompared to the literature.
基金supported by National Natural Science Foundation of China(Grant No.11171274).
文摘This paper studies a system of semi-linear fractional diffusion equations which arise in competitive predator-preymodels by replacing the second-order derivatives in the spatial variables with fractional derivatives of order less than two.Moving finite element methods are proposed to solve the system of fractional diffusion equations and the convergence rates of the methods are proved.Numerical examples are carried out to confirm the theoretical findings.Some applications in anomalous diffusive Lotka-Volterra and Michaelis-Menten-Holling predator-preymodels are studied.
基金Supported by the National Natural Science Foundation of China (No.70871084)Scientific Research Fund of Southwestern University of Finance and Economicsthe Specialized Research Fund for the Doctoral Program of Higher Education of China (No.200806360001)
文摘Using recursive method, this paper studies the queue size properties at any epoch n＋ in Geom/G/ I（E, SV） queueing model with feedback under LASDA （late arrival system with delayed access） setup. Some new results about the recursive expressions of queue size distribution at different epoch （n＋, n, n-） are obtained. Furthermore the important relations between stationary queue size distribution at different epochs are discovered. The results are different from the relations given in M/G/1 queueing system. The model discussed in this paper can be widely applied in many kinds of communications and computer network.
基金supported by National Natural Science Foundation of China (Grant Nos.10901027 and 11171274)Foundation of Hunan Educational Committee (Grant No. 10C0370)
文摘With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations （FPDEs）. The unconditional stability and convergence rates of 2 -a for time and r for space are proved when the method is used for the linear time FPDEs with a-th order time derivatives. Numerical exam-ples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method.
基金partly supported by SRF for ROCS, SEMsupported by a grant from the "project 211 (phase Ⅲ)" of the Southwestern University of Finance and Economics
文摘This paper develops and analyzes a moving mesh finite difference method for solving partial integro-differential equations. First, the time-dependent mapping of the coordinate transformation is approximated by a a piecewise linear function in time. Then, piecewise quadratic polynomial in space and an efficient method to discretize the memory term of the equation is designed using the moving mesh approach. In each time slice, a simple piecewise constant approximation of the integrand is used, and thus a quadrature is constructed for the memory term. The central finite difference scheme for space and the backward Euler scheme for time are used. The paper proves that the accumulation of the quadrature error is uniformly bounded and that the convergence of the method is second order in space and first order in time. Numerical experiments are carried out to confirm the theoretical predictions.
基金This work was supported By SWUFE's Key Subjects Construction Items Funds of 211 Project of the 11th Five-Year Plan
文摘Let G be a bounded open subset in the complex plane and let H 2(G)denote the Hardy space on G.We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1–1 with respect to the Lebesgue measure on?D and if the Riemann map belongs to the weak-star closure of the polynomials in H∞(W).Our main theorem states:in order that for each M∈Lat(M z),there exist u∈H∞(G)such that M=∨{uνH 2(G)},it is necessary and sufficient that the following hold:each component of G is a perfectly connected domain the harmonic measures of the components of G are mutually singular the set of polynomials is weak-star dense in H∞(G).Moreover,if G satisfies these conditions,then every M∈Lat(M z)is of the form uH 2(G),where u∈H∞(G)and the restriction of u to each of the components of G is either an inner function or zero.
基金supported by the Sichuan Youth Science and Technology Foundation(No.2014JQ0003)
文摘This paper deals with the global strong solution to the three-dimensional(3D)full compressible Navier-Stokes systems with vacuum. The authors provide a sufficient condition which requires that the Sobolev norm of the temperature and some norm of the divergence of the velocity are bounded, for the global regularity of strong solution to the 3D compressible Navier-Stokes equations. This result indicates that the divergence of velocity fields plays a dominant role in the blowup mechanism for the full compressible Navier-Stokes equations in three dimensions.
基金supported by Natural Science Foundation of USA(Grant Nos.DMS-0071976,DMS-0234078)the Southwestern University of Finance and Economics Third Period Construction Item Funds of the 211 Project(Grant No.211D3T06)
文摘The best breakdown point robustness is one of the most outstanding features of the univariate median.For this robustness property,the median,however,has to pay the price of a low effciency at normal and other light-tailed models.Affine equivariant multivariate analogues of the univariate median with high breakdown points were constructed in the past two decades.For the high breakdown robustness,most of them also have to sacrifice their effciency at normal and other models,nevertheless.The affine equivariant maximum depth estimator proposed and studied in this paper turns out to be an exception.Like the univariate median,it also possesses a highest breakdown point among all its multivariate competitors.Unlike the univariate median,it is also highly efficient relative to the sample mean at normal and various other distributions,overcoming the vital low-effciency shortcoming of the univariate and other multivariate generalized medians.The paper also studies the asymptotics of the estimator and establishes its limit distribution without symmetry and other strong assumptions that are typically imposed on the underlying distribution.
基金supported by the Natural Science Foundation of Fujian Province2017J01555,2017J01502,2017J01557 and 2019J01646the National NSF of China 11201077+1 种基金China Scholarship Fundthe Natural Science Foundation of Fujian Provincial Department of Education JAT160274
文摘In this paper,a two dimensional(2D)fractional Black-Scholes(FBS)model on two assets following independent geometric Lévy processes is solved numerically.A high order convergent implicit difference scheme is constructed and detailed numerical analysis is established.The fractional derivative is a quasidifferential operator,whose nonlocal nature yields a dense lower Hessenberg block coefficient matrix.In order to speed up calculation and save storage space,a fast bi-conjugate gradient stabilized(FBi-CGSTAB)method is proposed to solve the resultant linear system.Finally,one example with a known exact solution is provided to assess the effectiveness and efficiency of the presented fast numerical technique.The pricing of a European Call-on-Min option is showed in the other example,in which the influence of fractional derivative order and volatility on the 2D FBS model is revealed by comparing with the classical 2D B-S model.
