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Radial Basis Function Interpolation Methods And Their Application In Solving BSDEs

Posted on:2013-05-06Degree:MasterType:Thesis
Country:ChinaCandidate:P F LiFull Text:PDF
GTID:2230330374482626Subject:Probability theory and mathematical statistics
Abstract/Summary:PDF Full Text Request
Since Pardoux and Peng introduced the general form of backward stochas-tic differential equation(BSDE for short), this theory has been widely used in pricing problems of a large class of derivative securities and gained a big devel-opment. A large amount of problems in mathematical finance can be treated as a BSDE. However, it is well known that only a limited number of BSDE can be solved explicitly, so the numerical solutions of BSDE are very important. Many scholars have made great efforts to seek numerical solution for BSDE and got very good results. Peng extended the famous Fcynman-Kac formula to nonlinear case, this promoted the development of partial differential equation and broaden the way to solve BSDE.In this paper, we first present radial basis function interpolation meth-ods, including common radial basis functions, interpolation process and the coupling of radial basis function and polynomial, give a way to dynamically select the unknown parameter of radial basis function and do a large number of numerical experiments. Then we briefly introduce BSDE and its numerical solution. Based on the θ scheme proposed by Zhao, Chen and Peng, we use ra-dial basis function interpolation methods to approximate the value at relevant nodes when using Gauss-Hermite integral formula to calculus the conditional mathematical expectation. We do a series of numerical experiments to solve BSDE and the results verify our methods. Radial basis function interpolation does not need grids and partitions and has nothing to do with space dimen-sion, it can be easily used for the interpolation of high-dimensional data, so our method in this paper can be used to solve high-dimensional BSDE conve-niently.In the simulation of BSDEs, we compare the dynamic selection of unknown parameter of radial basis function with fixed parameter and other interpolation methods, the simulation results show that method with dynamic selection of unknown parameter of radial basis function has higher accuracy, this method can be used for numerical solving of BSDE.
Keywords/Search Tags:Radial basis function interpolation, BSDE, θscheme, Dynamic selection of unknown parameter, Gauss-Hcrmite integral formula
PDF Full Text Request
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