基本信息
講座題目：Some fundamentals of financial mathematics and recent research progress in American option pricing under regime switching models
報告人：諸頌平教授 伍倫貢大學
報告地點：數學樓第一報告廳
校内聯系人:韓月才 hanyc@jlu.edu.cn
講座内容及時間
課程摘要
As one of the most well-known examples in which mathematics has been successfully applied to social sciences, financial mathematics is a dynamic and vibrant research field where academics and practitioners in finance industry are constantly trying to broaden such applications. In this short course, I shall first, as Part 1 of the two parts, discuss some fundamental issues that quite often confuse beginners such as freshly enrolled PhD students or even ECRs (Earlier Career Researchers) in this field.
In Part 2, I shall present a recent research progress in adopting regime-switching model to price American put options: a generalized and highly efficient integral equation formulation has been developed with a goal of improving computational efficiency in mind, particularly when the number of regimes is large. Our achieved high efficiency is based on a newly proved theorem, which facilitates the decoupling of simultaneously coupled partial differential equation (PDE) sets so that they can be solved recursively at the numerical solution stage. Such a high efficiency is of course also fuelled further by the integral equation approach being characterized with its excellent trade-off between maximizing analytical tractability and minimizing numerical discretization. Some numerical examples are provided to demonstrate the implementation of the new approach and its efficiency.
To suit a broad range of students, the emphasis and majority of time during the five-lecture series will be on Part 1, so that the whole series contains some very fundamental concepts in financial mathematics (for undergraduate students), some principles of conducting scientific research (for master students) as well as some brief discussions and presentations of the most recent research outcomes from my research group at UoW (for master and PhD students).
報告人簡介
諸頌平教授是澳大利亞伍倫貢大學應用數學系資深教授。他于1987年12月畢業于密歇根大學并獲博士學位，累計在國際期刊和會議論文集上發表論文200 餘篇，吸引了澳大利亞研究理事會（ARC）和私營企業超過 200 萬美元的資金支持。此外，諸頌平教授共組織了兩次國際會議，并應邀在多個國際會議上發言。諸頌平教授的研究工作得到了國内外的廣泛認可，據ISI Web of Science 數據顯示，他的論文總引用次數超過 2000 次，H指數為27。
