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  • 學位論文

高精度算法在金融數學模型中的應用

On a High Order Numerical Method for Mathematical Models in Financial Engineering

指導教授 : 薛克民

摘要


本論文將類頻譜法運用在幾種金融工程中著名的模型並對其適用範圍、收斂 速度、數值計算的穩定性等方面進行探討。此方法相對於傳統作法被證實有其特 殊的優越性,尤其在特殊邊界問題上的運用。

並列摘要


The aim of this thesis is to address some mathematical issues on the application of pseudo spectral method on several important models in financial engineering, such as scope of application, speed of convergence, numerical stability, etc. This method has been proven superior with respect to the traditional ones especially for problems with special boundary conditions.

參考文獻


Numerical Solution of Initial-Boundary-Value Problems Using Radial Basis
Functions,” Faculty of Engineering Sciences GIK Institute of Engineering
Conditions in The Meshless Local Petrov–Galerkin Method,” Universidade
[9] Hans Munthe-Kaas, Tor Sorevik, “Multidimensional pseudo-spectral methods on
10] Genz, A., “A Lagrange Extrapolation Algorithm for Sequences of

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