Utility Based Pricing and Hedging in Incomplete Markets with Stochastic Preferences in a Unifying Framework of Admissibility

统一受理框架中具有随机偏好的不完全市场中基于效用的定价和对冲

• 批准号: 1515842
• 负责人: Oleksii Mostovyi
• 金额: $ 11.52万
• 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: 2015
• 资助国家: 美国
• 起止时间: 2015-09-15 至 2015-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1515842&HistoricalAwards=false
• 关键词: Utility; Based; Pricing; Hedging; Incomplete

The problems of pricing and hedging of financial instruments are of fundamental importance from both theoretical and practical sides of mathematical finance. In this research project, the investigator develops a novel framework and an approach for analysis of various notions of prices and hedging strategies in general models of financial markets. He aims to develop a utility-based pricing method for contingent claims with embedded payment streams. In a complete financial market every contingent claim can be replicated by a portfolio of the traded securities and therefore admits a unique arbitrage-free price, which is an initial value of the replicating strategy. In an incomplete market, to every contingent claim is associated an interval of arbitrage-free prices (unless the claim is replicable). In order to overcome the issue of non-uniqueness, alternative (equilibrium- or utility-based) approaches have been developed. The present project focuses on the probabilistic process-theoretic aspects of the problems of utility-based pricing and hedging of contingent claims and income streams. The aim of this project is twofold -- investigation of different notions of prices, hedging strategies, and relationships between them, in the settings that include stochastic utility (as a natural generalization of the utility function concept), and a construction of a utility-based pricing methodology for the contingent claims with embedded payment streams, in incomplete continuous-time models of financial markets. A novel concept of a unified framework of admissibility is introduced for the accomplishment of the goals described above. The unified framework permits consideration of the underlying utility maximization problems with different types of budget constraints, in one formulation. On the technical level, the analysis relies on the existing and new techniques drawing on the general theory of semimartingales, stochastic optimal control, and convex analysis. The approach provides a firm ground for an extension of the scope of applicability of the utility-based pricing techniques and for asymptotic expansions of the utility-based prices and hedging strategies.

从数学金融的理论和实践方面，金融工具的定价和对冲问题至关重要。 在该研究项目中，研究人员开发了一种新颖的框架，并在金融市场的一般模型中对各种价格概念和对冲策略进行分析。 他的目标是开发一种基于公用事业的定价方法，用于带有嵌入式支付流的有意义的索赔。在整个金融市场中，每个有可能的索赔都可以由交易证券的投资组合复制，因此承认无套利的价格，这是复制策略的初始价值。 在不完整的市场中，每个有索赔都与无套利价格的间隔相关联（除非索赔可复制）。 为了克服非唯一性问题，已经开发了替代性（基于平衡或实用性的）方法。 本项目的重点是基于公用事业的定价和应有索赔和收入流的概率过程理论方面。 该项目的目的是双重的 - 在包括随机效用的设置中对不同的价格，对冲策略及其之间的关系进行调查（作为随机效用的设置（作为效用函数概念的自然概括），以及在不满的持续时间的财务市场中，以嵌入式支付方式进行基于公用事业的定价方法来构建，用于嵌入式支付流的情况下。 为实现上述目标的实现引入了一个统一的可接受性框架的新颖概念。 统一框架允许在一种公式中考虑具有不同类型的预算约束的潜在实用性最大化问题。 在技​​术层面上，分析依赖于现有的和新技术，这些技术利用了半明星，随机最佳控制和凸分析的一般理论。 该方法为扩展基于公用事业的定价技术的适用范围以及基于公用事业价格和对冲策略的渐近扩展提供了牢固的基础。