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

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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.