NSF Award
2205751
This project is concerned with the analysis of dynamical systems whose components are not perfectly observable at all times. The examples of such systems are numerous: e.g., any received radio signal is subject to noise, the temperature in some parts of the ocean may not be known exactly at all times but is correlated with the known temperatures in other locations, a price of a house may not be known precisely before it is sold but it is correlated with the transaction prices of similar properties, etc. In this context, the PI will focus on two questions: how to efficiently estimate the unknown parameters of such systems given historical data, and how to choose these parameters in order to maximize a given objective. The concrete applications that motivate this work arise from Finance and Economics: namely, from the problem of estimating the parameters of unobserved price process of a financial asset (e.g., a stock price between transactions) and from the question of optimal contract design (e.g., what is the optimal structure of fees that brokers should charge to their clients, if the latter have proprietary knowledge about the market). In addition, the results of this work will contribute to the general methodology for estimation and optimization of partially observed dynamical systems and, hence, be applicable to many other problems arising in social and natural sciences. Participation in the project will provide good training opportunities for both graduate and undergraduate students.<br/><br/>This project consists of two lines of research on the stochastic dynamical systems with partial observations. The first is concerned with the problem of statistical inference of unknown parameters in partially observed diffusion models. In particular, the PI will investigate the large-sample properties of maximum likelihood estimators (MLEs) for partially observed diffusion models, and will develop approximation methods in the case of degenerate diffusions where the likelihood function cannot be computed directly. This research is motivated by the problem of estimating the unknown parameters in latent price models of market microstructure. The second line of research is concerned with the design of optimal contracts in the presence of information asymmetry between the principal and the agent. The information asymmetry that the PI will consider is different from the classical moral hazard type and stems from the difference in the exogenously given filtrations to which the actions of the principal and of the agent are adapted. Such optimal contract models lead to challenging stochastic control problems with informational constraints. The second line of research is motivated, in particular, by the problem of designing optimal brokerage fees in financial markets. The results of the proposed research will make significant contributions to both theory and applications. The first line of research (concerned with MLEs) is expected to advance the mathematical foundations of Statistics and to develop new computational methods for parameter estimation in partially observed systems. These results will be applied to specific problems in market microstructure (such as the reconstruction of the true unobserved price of an asset and the estimation of price impact) as well as to inference problems in other areas (e.g., Computational Neuroscience). The results of the second line of research (concerned with optimal contracts) will contribute to the theories of stochastic control and optimal contract design. These theoretical results, in particular, can be used to develop better understanding of the effects of intermediaries (brokers) on the financial markets.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
