University - Industry Cooperative Research Programs in the Mathematical Sciences: Columbia University-Morgan Stanley Post-Doctoral Research Fellowship

Karatzas DMS-9704505我们建议培训一名博士后研究助理，为期两年，学习现代金融的各种数学和计算方面的知识，结合摩根士丹利固定收益研究小组的实力和哥伦比亚大学教职员工的数学专业知识。博士后研究员将能够从这两个小组的专业知识中受益，并将成为他们之间知识转移的催化剂。这位博士后将帮助开发一个数学框架，用于对利率敏感型(固定收益)工具上的美国式衍生品证券进行估值，并开发准确而快速的数值技术。这一问题具有相当重要的实际意义，需要先进的数学工具，如随机微分方程、最优停车、偏微分方程组和蒙特卡罗模拟等。这个项目由MPS多学科活动办公室(OMA)和数学科学部(DMS)共同支持。

Karatzas DMS-9704505 We propose to train a Post-Doctoral Research Associate, for two years, in the various mathematical and computational aspects of modern Finance, combining the strength of Morgan-Stanley's fixed income research group with the mathematical ewxpertise of the Columbia University faculty. The Post-Doctoral Fellow will be able to benefit from the expertise of both groups, and will act as catalyst for transfer of knowledge between them. The Post-Doctoral Fellow will be expected to help develop a mathematical framework for the valuation of American-style derivative securities on interest-sensitive (fixed-income) instruments, and to develop accurate and fast numerical techniques. The problem is of considerable practical importance, and requires advanced mathematical tools, such as stochastic differential equations, martingales and optimal stopping, partial differential equations and Monte-Carlo simulations. Department of Mathematics, Columbia University, New York, NY Morgan-Stanley & Co., Incorporated, New York, NY This project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS)