Optimal Portfolio and Model Selection in Financial Markets

金融市场中的最优投资组合和模型选择

• 批准号: 0099549
• 负责人: Jaksa Cvitanic
• 金额: $ 9万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-15 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0099549&HistoricalAwards=false
• 关键词: Optimal; Portfolio; Model; Selection; Financial

Pang, Jong-ShiFrom: Jaksa Cvitanic [[e-mail]]Sent: Monday, July 02, 2001 4:33 AMTo: Pang, Jong-ShiSubject: Re: your mailDear Dr. Pang,I enclose here the abstract for my proposal.Let me know , please, if it's O.K.Sincerely,Jaksa Cvitanic------ Principal Investigator: JAKSA CVITANICResearch is proposed on various aspects of the modern theory of financial markets and related mathematical problems of stochastic analysis, filtering and control. Issues that will be studied involve:(i) finding algorithms to compute the diffusion term ofthe optimal wealth/hedging process, and related questionsabout Martingale Representation Property and MalliavinCalculus;(ii) questions on maximizing Stochastic DifferentialUtility and connections to Forward-Backward Stochastic Differential Equations and problems of incomplete/asymmetric information;(iii) analytical and numerical methods for finding optimalportfolio/consumption investment for retirement, in general diffusion models;(iv) theory of utility maximization/risk minimization ingeneral semimartingale models of markets with frictions;(v) filtering and calibration of stochastic volatility models;(vi) optimal design of executive compensation.It is expected that tools from stochastic analysis and martingaletheory, convex duality theory, functional analysis, stochastic control, Monte Carlo/simulation methods, will prove valuable in the resolution of these questions, sometimes requiring development of new tools, thus enhancing the understanding of both the theoretical and applied aspects of these fields.The optimal portfolio selection and consumption selection is the theory that provides answers to the question of how to allocate money between investing in different assets in financial markets, and consuming it in order to buy various goods. The theory has been developed in almost full generality by now. However, it depends on a mathematical model of the markets, and our ability to estimate the model parameters. For example, correct pricing of complex financial contracts, such as exotic options, depends on how well we can estimate the "volatility" (riskiness) of the stock on which the option is written.One of the problems we propose to study is how to do this estimation by using observed stock prices. Similarly, the problem of actually computing the corresponding optimal trading strategies has not been resolved in general. The algorithms that are commonly used today typically do not work wellin more complex and realistic models for financial markets, that are becoming a standard, due to the increased sophistication of market modelers. Thus, it is important to explore new analytical and computational methods for finding optimal trading strategies, some of which are suggested in this proposal. Similar methods are suggested for exploring important problem of how a firm should compensate its executive so that the resulting behavior of the executive is optimal.

Pang，Jong-Shim发件人：Jaksa Cvitanic[[e-mail]]发送时间：2001年7月2日4：33 AM收件人：Pang，Jong-Shie主题：Re：您的邮件尊敬的Pang博士，我在这里附上了我的提案摘要。请让我知道，如果可以的话，请让我知道Jaksa Cvitanic-首席研究员：Jaksa CVITANIC研究是关于现代金融市场理论的各个方面以及随机分析、过滤和控制的相关数学问题。将研究的问题包括：(I)寻找算法来计算最优财富/套期保值过程的扩散项，以及有关鞅表示性质和Malliavin演算的相关问题；(Ii)关于随机微分效用最大化的问题，以及与前向向后随机微分方程的联系和不完全/不对称信息问题；(Iii)在一般扩散模型中寻找退休的最优投资组合/消费投资的分析和数值方法；(Iv)效用最大化/风险最小化理论在有摩擦的市场的一般半鞅模型中；(V)随机波动模型的过滤和校准；(Vi)高管薪酬的最优设计。预期来自随机分析和鞅理论、凸对偶理论、泛函分析、随机控制、蒙特卡罗/模拟方法的工具将被证明在解决这些问题方面有价值，有时需要开发新的工具，从而加深对这些领域的理论和应用方面的理解。最优投资组合选择和消费选择是为如何在金融市场上投资不同的资产，以及为了购买不同的商品而消费之间的资金分配问题提供答案的理论。到目前为止，这一理论已经发展到几乎完全概括的地步。然而，这取决于市场的数学模型，以及我们估计模型参数的能力。例如，复杂金融合约的正确定价，如奇异期权，取决于我们能多好地估计期权所在股票的“波动性”(风险)。我们建议研究的问题之一是如何利用观察到的股票价格进行这种估计。同样，实际计算相应的最优交易策略的问题也没有得到普遍解决。由于市场建模师的日益成熟，目前常用的算法在更复杂、更现实的金融市场模型中通常不能很好地发挥作用，这些模型正在成为一种标准。因此，重要的是探索新的分析和计算方法来寻找最优的交易策略，其中一些建议在本提案中提出。类似的方法也被用来探讨公司应该如何补偿其高管的重要问题，从而使高管的行为是最优的。