Collaborative Research: Applications of Stochastic Analysis to Models of Multi-Agent Interactions

连续时间契约理论的最新进展，其中一些来自于研究者之前的工作，以及均衡理论和流动性建模的进展，被应用于开发更现实的多个经济主体相互作用的模型。特别地，讨论了两家企业间合资企业的最优设计，即进入/退出项目的最优时间、每个企业应该投入的最优努力以及他们应该如何分享利润/损失，从而将经典实物期权理论扩展到两个企业的情况。本文提出了寻找经理人最优报酬的新模型，其中经理人可能比投资者拥有更好的信息，而投资者可能以一定的成本获得更好的信息。为了研究影响股票市场波动率和风险溢价的因素，本文分析了多主体金融市场均衡时价格的全局属性。此外，调查人员还模拟了由于流动性变化（例如在快速高频交易员存在的情况下），价格如何在当地演变。最后，在一个有许多相互作用的代理的市场模型中，该项目探讨了当代理数量增加时，平均违约数量和平均损失如何在极限下演变。鉴于最近金融市场危机的原因之一是交易员和管理人员的薪酬方式，这个项目显得尤为及时。这将有助于深入了解哪种类型的补偿方案对有关各方和整个社会都是最佳的。如果要防止未来发生类似的危机，另一个需要更好理解的问题是，由于许多代理人的相互作用，市场如何演变，以及流动性缺乏如何影响市场参与者的行为和价格。特别是，这项研究揭示了资产价格的形成，投资组合策略，在有许多代理人的市场中可以预期的违约频率，以及在不同程度流动性的市场中价格是如何形成的。因此，该项目的结果将阐明在监管金融市场薪酬和监管整个金融业时应重点关注哪些问题。

Recent advances in continuous-time contract theory, some of which have come out from the prior work of the investigators, as well as advances in equilibrium theory and in modeling liquidity, are applied in order to develop more realistic models of interactions of multiple economic agents. In particular, optimal design of joint ventures between two firms is addressed, that is, the optimal time to enter/exit a project, the optimal effort each should invest in it, and how they should share the profits/losses, thus extending the classical real options theory to the case of two agents. New models for finding optimal compensation to managers are developed, in which the manager may have better information than the investors, and in which the investors may acquire better information at a cost. Global properties of prices formed in equilibrium of financial markets with many agents are analyzed, in order to study what factors influence the volatility and the risk premium of the stock market. In addition, the investigators model how prices locally evolve due to changes in liquidity, for example in the presence of fast high-frequency traders. Finally, in a model of a market with many interacting agents, the project explores how the average number of defaults and average loss evolve in the limit when the number of agents grows.This project is particularly timely given that one of the reasons for the recent crisis in financial markets is the way traders and managers have been compensated. It will help provide insight into what types of compensation schemes are optimal for the parties involved and for the society in general. Another issue that needs better understanding if a similar crisis is to be prevented in the future, is how the markets evolve due to the interaction of many agents, and how lack of liquidity influences the behavior of the market participants and the prices. In particular, this research sheds light on the formation of asset prices, on portfolio strategies, and on the frequency of defaults that can be expected in markets with many agents, as well as how prices are formed in markets with varying degrees of liquidity. Thus, the results of the project will shed light on which issues to focus on when regulating compensation in financial markets and regulating the financial industry in general.