Stochastic Models of Asset Valuation in Markets with Frictions

有摩擦市场中资产估值的随机模型

• 批准号: 0102909
• 负责人: Thaleia Zariphopoulou
• 金额: $ 18万
• 依托单位: University of Texas at Austin
• 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: 2001-08-01 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0102909&HistoricalAwards=false
• 关键词: Stochastic; Models; Asset; Valuation; Markets

DMS 0102909PI: Thaleia ZariphopoulouIn most market models, the classical assumption of a perfect market is not satisfied. The PI proposes to continue her research program to develop methods to study valuation problems in incomplete markets, concetrated in the following class of applications: i) optimal asset allocation under market frictions the goal being to derive and analyze the optimal risky demand and to represent the value function in terms of distorted measures, ii) valuation of derivatives written on nontraded assets with the goal to use utility-based pricing methodology to specify the hedging strategies and to expole their role in risk aggregation, iii) dynamic hedging of volatility risks the goal being to specify the arbitrage-free components of the implied volatility process and to study their implications to the dynamic management of volatility risks, andiv) asset valuation under irreversible decisions with the goals being to evaluate early exercise instruments under constraints related to irreversible decisions and to analyze the impact of irreversibilities to prices and optimal demand. The technical tools come from stochastic analysis, stochastic control and nonlinear partial differential equations.In most market settings, the classical assumption of market completeness is not satisfied and, therefore, the traditional approach of perfect replication cannot be applied. It becomes hence necessary to review the pricing and risk management concepts. The first step is the development of a unified framework to analyze the inherent market risks, and identify the components that can be hedged away and the ones that cannot. The second step is the establishment of a coherent method to price the unhedgeable risks in order to achieve effective risk management. The PI proposes to continue her work in market models with frictions along the aforementioned two general directions. The proposed methodologies relyheavily on the classical economic principles of utility theory whichreflect the investors' preferences towards the risks that cannot beeliminated. Among others, the PI proposes to study models of assetallocation, derivative pricing and risk management under various marketfrictions including stochastic volatility, nontraded assets andirreversible management policies.

DMS 0102909 PI：Thaleia Zariphopoulou在大多数市场模型中，完美市场的经典假设并不满足。PI建议继续她的研究计划，开发研究不完整市场中估值问题的方法，集中在以下类别的应用中：i）市场摩擦下的最优资产配置目标是导出和分析最优风险需求，并以扭曲度量表示价值函数，ii）对非交易资产上的衍生工具进行估值，目的是使用基于效用的定价方法来指定对冲策略并扩展其在风险汇总中的作用，iii）波动风险的动态对冲目标是指定隐含波动过程的无仲裁成分，并研究其对波动风险动态管理的影响，andiv）不可逆决策下的资产估值，目标是在与不可逆决策相关的约束条件下评估早期执行工具，并分析不可逆性对价格和最优需求的影响。技术工具来自随机分析、随机控制和非线性偏微分方程。在大多数市场环境中，经典的市场完全性假设不被满足，因此传统的完美复制方法不能应用。因此，有必要审查定价和风险管理概念。 第一步是建立一个统一的框架来分析固有的市场风险，并确定哪些成分可以对冲，哪些不能。第二步是建立一个连贯的方法来定价不可对冲的风险，以实现有效的风险管理。PI建议继续她的工作，在市场模型与摩擦沿着上述两个一般方向。所提出的方法在很大程度上依赖于效用理论的经典经济学原理，该原理反映了投资者对无法消除的风险的偏好。其中，PI建议研究各种市场摩擦下的资产配置，衍生品定价和风险管理模型，包括随机波动，非交易资产和不可逆的管理政策。