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Development of Multilevel Monte Carlo Algorithms for Mathematical Finance

数学金融多级蒙特卡罗算法的开发

基本信息

批准号：
EP/E031455/1
负责人：
Mike Giles
金额：
$ 9.5万
依托单位：
University of Oxford
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2007
资助国家：
英国
起止时间：
2007 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FE031455%2F1
关键词：
Development Multilevel Monte Carlo Algorithms

项目摘要

This Springboard Fellowship will help me enormously in my mid-career move into computational finance after 20 years of computational fluid dynamics, simulating the flow through aircraft gas turbine engines. The research topic concerns the pricing of financial derivatives options (based on equities, commodities, interest rates and exchange rates) using Monte Carlo methods which evaluate the average outcome from multiple simulations of possible future evolution subject to random inputs. This research area, the solution of stochastic differential equations, is a major growth area in mathematics, and it underpins much of the everyday working of the major banks in London, which in turn form a large part of the UK economy.Six months ago, I had an idea which signifiantly reduces the computational cost of the Monte Carlo calculations required to achieve a given accuracy. My preliminary research results, and numerical tests on model problems, are very encouraging. It has been well received by leading academic figures and has already led to invitations for three university presentations and four seminars at investment banks. My objective with this Fellowship proposal is to build on this initial success by further developing the numerical technique, which I refer to as the multilevel Monte Carlo method, to enhance its performance and make it competitive against the leading methods used today in the industry. Alongside the research itself, a major goal of the fellowship is to build collaborations with key academics worldwide and with leading banks in London. My aim is that these should continue long after the end of the Fellowship, with the banks being my major source of funding for subsequent research. Also, as I am still very new to this field of research, there are deficiencies in my understanding of the stochastic analysis theory which underpins this field and I will work to address these.

这个跳板奖学金将极大地帮助我在职业生涯中期进入计算金融领域，在我从事计算流体力学20年后，模拟了飞机燃气涡轮机发动机的流动。研究主题涉及金融衍生品期权（基于股票，商品，利率和汇率）的定价，使用蒙特卡罗方法评估随机输入下可能的未来演变的多次模拟的平均结果。这个研究领域，随机微分方程的解决方案，是数学的一个主要增长领域，它支撑了伦敦主要银行的日常工作，这反过来又形成了英国经济的很大一部分。六个月前，我有一个想法，这显着降低了蒙特卡洛计算所需的计算成本，以达到给定的精度。我的初步研究结果，以及对模型问题的数值试验，是非常令人鼓舞的。它受到了学术界知名人士的好评，并已被邀请参加三次大学演讲和四次投资银行研讨会。我的目标是通过进一步发展数值技术（我称之为多级蒙特卡罗方法）来建立这个初步的成功，以提高其性能，并使其与当今行业中使用的领先方法竞争。除了研究本身，奖学金的一个主要目标是与世界各地的主要学者和伦敦的主要银行建立合作关系。我的目标是，在奖学金结束后，这些活动应该继续很长一段时间，银行是我后续研究的主要资金来源。此外，由于我对这一研究领域还很陌生，因此我对支撑这一领域的随机分析理论的理解存在不足，我将努力解决这些问题。

项目成果

期刊论文数量（9）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Monte Carlo and Quasi-Monte Carlo Methods 2012

蒙特卡罗和准蒙特卡罗方法 2012

DOI：
10.1007/978-3-642-41095-6_4
发表时间：
2013
期刊：
影响因子：
0
作者：
Giles M
通讯作者：
Giles M

Multilevel Monte Carlo for exponential Lévy models

指数 Lévy 模型的多级蒙特卡罗

DOI：
10.1007/s00780-017-0341-7
发表时间：
2017
期刊：
Finance and Stochastics
影响因子：
1.7
作者：
Giles M
通讯作者：
Giles M

Multilevel and Quasi Monte Carlo Methods for the Calculation of the Expected Value of Partial Perfect Information.

DOI：
10.1177/0272989x211026305
发表时间：
2022-03
期刊：
Medical decision making : an international journal of the Society for Medical Decision Making
影响因子：
0
作者：
Fang W;Wang Z;Giles MB;Jackson CH;Welton NJ;Andrieu C;Thom H
通讯作者：
Thom H

Multilevel Monte Carlo methods