Stochastic Models of Asset Valuation in Markets with Frictions

University Of Texas At Austin, Austin TX

Investigators

Abstract

DMS 0102909 PI: Thaleia Zariphopoulou In 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, and iv) 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 rely heavily on the classical economic principles of utility theory which reflect the investors' preferences towards the risks that cannot be eliminated. Among others, the PI proposes to study models of asset allocation, derivative pricing and risk management under various market frictions including stochastic volatility, nontraded assets and irreversible management policies.