1,725,036 research outputs found
L-INFINITY-ERROR ESTIMATES FOR MIXED METHODS FOR SEMILINEAR 2ND-ORDER ELLIPTIC-EQUATIONS
No full textopen1115sci
SECOND-ORDER FINITE DIFFERENCE METHOD FOR OPTION PRICING UNDER JUMP-DIFFUSION MODELS
No full textWe develop a finite difference method to solve partial integro-differential equations which describe the behavior of option prices under jump-diffusion models. With localization to a bounded domain of the spatial variable, these equations are discretized on uniform grid points over a finite domain of time and spatial variables. The proposed method is based on three time levels and leads to linear systems with tridiagonal matrices. In this paper the stability of the proposed method and the second-order convergence rate with respect to a discrete l(2)-norm are proved. Numerical results obtained with European put options under the Merton and Kou models show the behaviors of the stability and the second-order convergence rate.open112219sciescopu
A collocation method for the Gurtin-MacCamy equation with finite life-span
No full textA collocation method along the characteristics for a stiff problem arising from population dynamics is proposed and analyzed. It is a fourth order implicit Runge-Kutta method of two stage to the integration of the ODE along the characteristics, whose collocation points are zeros of the linearly transformed Legendre monic polynomial. Nonnegativity of the numerical solutions is shown. The stability of the method is discussed. It is proven that the scheme is convergent at a fourth order rate in the maximum norm. Several numerical examples are presented.open1124sciescopu
A SECOND-ORDER TRIDIAGONAL METHOD FOR AMERICAN OPTIONS UNDER JUMP-DIFFUSION MODELS
No full textWe propose an implicit numerical method for pricing American options where the underlying asset follows a jump-diffusion model. Using the fact that the prices of American options are given by linear complementarity problems (LCPs), we combine an implicit finite difference method with an operator splitting method. The proposed method is constructed on three time levels, and the operator splitting method is used to treat American constraints. We concentrate on the formulation of the numerical method which leads to linear systems with tridiagonal coefficient matrices. Numerical experiments show that the implicit method has the second-order convergence rate, and the prices of American options can be obtained in a fraction of a second on a computer.open111820sciescopu
Parameter estimation in nonlinear age-dependent population dynamics
No full textThis paper studies a parameter estimation problem for the Gurtin-MacCamy equation, which is a nonlinear model of age-dependent population dynamics. In estimating parameters such as the death rate and the fertility which depend on the age and the total population from a set of fully discrete observations of the population, we use a backward finite-difference scheme. The function-space parameter estimation convergence (FSPEC) of this scheme is proved and numerical simulations are performed.X116sciescopu
State-wise Potential Description for Modeling Relationships between Distant Nodes in Markov Random Fields
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A DIRECT SOLVER FOR THE LEGENDRE TAU APPROXIMATION FOR THE TWO-DIMENSIONAL POISSON PROBLEM
No full text11scopu
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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