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Numerical studies of di{uFB00}erential equations and their applications in financial mathematics / Muner Mustafa Abou Hasan ; Supervised Laila F. Abdelal , Nasser H. Sweilam , Malak M. Rizk

By: Contributor(s): Material type: TextTextLanguage: English Publication details: Cairo : Muner Mustafa Abou Hasan , 2014Description: 81 P. : charts ; 25cmOther title:
  • دراسات عددية للمعادلات التفاضلية وتطبيقاتها في الرياضيات المالية [Added title page title]
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  • Issued also as CD
Dissertation note: Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics Summary: This thesis is a contribution on numerical solutions for systems of ordinary di{uFB00}erential equations (ODEs) and Black-Scholes parabolic partial di{uFB00}erential equations. Two di{uFB00}erent numerical approaches are presented in this thesis to solve general Black-Scholes equation. The {uFB01}rst one is: The modi{uFB01}ed Dzyadyk{u2019}s approximation iterative method (MDAI-metod) depending on Hermite poly- nomials, which is used to solve sti{uFB00} systems of ordinary di{uFB00}erential equations, then it is also used to solve parabolic partial di{uFB00}erential equations. Using MDAI method to solve partial di{uFB00}erential equations (PDEs) is facilitated by the method of lines which reduce the problem to solve a system of sti{uFB00} ordinary di{uFB00}erential equations. The stability analysis of this method is presented. The second method is: the non-uniform {uFB01}nite di{uFB00}erence method which is used to {uFB01}nd value of European and American put options using Black-Scholes Model. Stability of this method and the truncation error are studied here
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Thesis Thesis قاعة الرسائل الجامعية - الدور الاول المكتبة المركزبة الجديدة - جامعة القاهرة Cai01.12.17.M.Sc.2014.Mu.N (Browse shelf(Opens below)) Not for loan 01010110066029000
CD - Rom CD - Rom مخـــزن الرســائل الجـــامعية - البدروم المكتبة المركزبة الجديدة - جامعة القاهرة Cai01.12.17.M.Sc.2014.Mu.N (Browse shelf(Opens below)) 66029.CD Not for loan 01020110066029000

Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics

This thesis is a contribution on numerical solutions for systems of ordinary di{uFB00}erential equations (ODEs) and Black-Scholes parabolic partial di{uFB00}erential equations. Two di{uFB00}erent numerical approaches are presented in this thesis to solve general Black-Scholes equation. The {uFB01}rst one is: The modi{uFB01}ed Dzyadyk{u2019}s approximation iterative method (MDAI-metod) depending on Hermite poly- nomials, which is used to solve sti{uFB00} systems of ordinary di{uFB00}erential equations, then it is also used to solve parabolic partial di{uFB00}erential equations. Using MDAI method to solve partial di{uFB00}erential equations (PDEs) is facilitated by the method of lines which reduce the problem to solve a system of sti{uFB00} ordinary di{uFB00}erential equations. The stability analysis of this method is presented. The second method is: the non-uniform {uFB01}nite di{uFB00}erence method which is used to {uFB01}nd value of European and American put options using Black-Scholes Model. Stability of this method and the truncation error are studied here

Issued also as CD

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