Stochastic Analysis of Large Investors

大投资者的随机分析

• 批准号: 1651180
• 负责人: Scott Robertson
• 金额: $ 4.27万
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1651180&HistoricalAwards=false
• 关键词: Stochastic; Analysis; Large; Investors

Robinson1312419 The investigator and his colleagues use asymptotic methods from stochastic analysis to provide a comprehensive study of large investors in derivatives markets. The specific goals are first to identify characteristics of both the investor and the market that endogenously lead to large holdings, and second to determine the effects of large positions on pricing, price impact, portfolio optimization, and risk management. Because large positions induce extreme sensitivity to rare unexpected events, the theory of Large Deviations is well suited for this analysis. In particular, using Large Deviations in conjunction with utility-based theory on optimal position sizes, the investigator studies when, if ever, a risk-averse agent acting in an incomplete market should take a large position in a non-traded risky asset. Regarding the issue of pricing and hedging, it is well known that in incomplete markets investor preferences affect the price at which one is willing to buy a claim. Typically, closed-form expressions for utility based prices are unavailable and some approximation is necessary. Existing approximations are only valid for small position sizes and thus large holdings approximations provide a natural counterpart. In addition to determining asymptotic prices, the investigator identifies the key components of the investor's utility that drive such prices. Lastly, examples show that large positions arise in conjunction with asymptotically complete markets: the investigator thus seeks to extend this notion beyond the current one, which focuses on weak convergence of asset price laws, to a more natural notion in terms of the asymptotic ability to hedge. Once extended, questions regarding continuity with respect to market completeness are considered. From a rigorous mathematical perspective, the investigator seeks to understand the rapid growth in over-the-counter derivatives markets during the previous two decades. Given the complexity of many of these products, it is not clear why a bank, or some other financial institution, would wish to take on a large position in a claim, especially given the lack of perfect hedging strategies or liquid markets. The investigator thus studies when, if ever, a financial institution should own a significant notional amount of a derivative contract. Additionally, given such a position, the investigator aims to determine the impacts in terms of pricing, hedging, and over-all risk that a financial institution faces.

Robinson1312419调查员及其同事使用随机分析的渐近方法提供对衍生品市场中大型投资者的全面研究。 具体目标是首先确定投资者和内在导致大量持股的市场的特征，其次是确定大型头寸对定价，价格影响，投资组合优化和风险管理的影响。 由于大型位置对罕见意外事件产生极端敏感性，因此大偏差的理论非常适合该分析。 特别是，将大偏差与基于公用事业的最佳位置大小的理论结合使用，研究人员研究了在不完整市场中作用的抗风险代理时，应在非交易风险资产中处于较大的位置。 关于定价和对冲问题，众所周知，在不完整的市场中，投资者的偏好会影响人们愿意购买索赔的价格。 通常，基于公用事业价格的封闭式表达式不可用，并且需要一些近似值。 现有的近似仅适用于小位置大小，因此大容量近似值提供了自然的对应物。 除了确定渐近价格外，研究人员还确定了投资者效用的关键组成部分，这些效用可以推动此类价格。 最后，实例表明，大型立场与渐近完整的市场结合出现：因此，研究人员试图将此概念范围扩展到当前的概念之外，该概念的重点是资产价格法律的弱收敛性，以对冲的渐近能力来更自然的概念。 一旦扩展，就考虑了有关市场完整性的有关连续性的问题。 从严格的数学角度来看，研究人员试图了解过去二十年来非处方衍生品市场的快速增长。 考虑到许多这些产品的复杂性，尚不清楚银行或其他一些金融机构为什么希望在索赔中处于巨大地位，尤其是考虑到缺乏完美的对冲策略或液体市场。 因此，研究人员研究金融机构应拥有大量名义数量的衍生合同。 此外，鉴于这样的职位，研究人员旨在确定金融机构面临的定价，对冲和过度风险的影响。