Asymptotic Methods in Financial Mathematics

金融数学中的渐近方法

• 批准号: 0306357
• 负责人: K. Ronnie Sircar
• 金额: $ 18.6万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-01 至 2006-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0306357&HistoricalAwards=false
• 关键词: Asymptotic; Methods; Financial; Mathematics

This project studies some problems in financial mathematics related to stochastic volatility models and portfolio optimization. The specific problems under consideration here are 1) identification and analysis of time-scales in market volatility; 2) analysis of "alternative" mechanisms for pricing and hedging derivative securities via stochastic control methods, in particular to model "crash-o-phobia"; 3) optimal investment decisions under stochastic stock price models incorporating asymmetry in returns distributions.The spectacular growth in the size of the financial derivatives market over the last thirty years (currently it has a turnover of trillions of dollars in the US) plus recent infamous (and equally spectacular) risk (mis)management disasters, such as the Barings, Orange County and Long Term Capital Management fiascos, have created an urgent need for smart mathematical and computational models to quantify the respective risks and rewards of such investments. This continuing project aims to build on the methodology introduced by Black, Scholes and Merton, to take into account the uncertain nature of market volatility. Mathematical and computational tools are combined with statistical analysis of past prices to produce formulas and software that better understand the potentially serious consequences of changing volatility for portfolios. This issue is important for investors from large trading institutions to individuals with pension funds.

本计画研究金融数学中与随机波动率模型及投资组合最佳化相关之问题。这里考虑的具体问题是：1）识别和分析市场波动的时间尺度; 2）通过随机控制方法分析衍生证券定价和对冲的“替代”机制，特别是模拟“崩溃恐惧症”;第三章最优投资决策的随机股票价格模型，包括不对称的回报分布。惊人的增长，在规模的金融衍生品市场在过去三十年中的交易额（目前在美国其交易额为数万亿美元），加上最近臭名昭著的（同样壮观的）风险（mis）管理灾难，如巴林银行、橙子县和长期资本管理公司的惨败，已经迫切需要智能数学和计算模型来量化这些投资的相应风险和回报。这个持续的项目旨在建立在布莱克，斯科尔斯和默顿介绍的方法，考虑到市场波动的不确定性。数学和计算工具与过去价格的统计分析相结合，产生公式和软件，更好地理解投资组合波动性变化的潜在严重后果。这个问题对从大型交易机构到拥有养老基金的个人的投资者都很重要。