Stochastic Models of Asset Valuation in Markets with Frictions

在大多数市场模型中，经典的完美市场假设是不被满足的。PI建议继续她的研究计划，以开发研究不完全市场估值问题的方法，集中在以下应用类别：I)市场摩擦下的最优资产配置，目标是推导和分析最优风险需求，并以扭曲的度量方式表示价值函数，ii)非交易资产衍生品的估值，目标是使用基于效用的定价方法来指定对冲策略，并探索它们在风险聚集中的作用。Iii)波动率风险的动态对冲，目标是明确隐含波动率过程的无套利成分，并研究它们对波动率风险动态管理的影响，以及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下评估早期行权工具，并分析不可逆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，市场完备性的经典假设不被满足，因此，传统的完全复制方法不能适用。因此，有必要审查定价和风险管理概念。第一步是开发一个统一的框架来分析固有的市场风险，并确定可以对冲和不能对冲的组成部分。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建议在市场模型中继续她的工作，在上述两个一般方向上存在摩擦。所提出的方法在很大程度上依赖于效用理论的经典经济原则，这些原则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转的管理政策。

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.