Asymptotics for large stochastic systems
- Large, interacting stochastic systems appear in many facets of today's world and are of broad importance. Examples include the banking system, financial markets, electric power grids, engineering systems, health care, and social networks. Due to their scale, complexity, and large amounts of data, analyzing such systems is inherently challenging. This dissertation develops computational methods for simulation and optimization for such large systems. The computational methods are built upon weak convergence results which can be used to approximate a large system. An ecient Monte Carlo approximation for the fast simulation of large systems is developed. The Monte Carlo approximation is built upon a dynamic law of large numbers and dynamic central limit theorem. This same approximation is used to approximate optimization problems for large stochastic systems. The solution to the approximate optimization problem, called the "asymptotically optimal portfolio", yields accurate and computationally cheap solutions to large-scale optimization problems for such systems. In particular, the work in this dissertation is motivated by the modeling of large pools of financial loans. Financial institutions, government-sponsored enterprises such as Fannie Mae, and asset-backed security investors are often exposed to delinquency and prepayment risk from large numbers of loans. Examples include mortgages, credit cards, auto, commercial, real estate, student, and small business loans. Due to the size of such loan pools and the potentially long maturities of their cashflows, the measurement and management of these exposures are computationally expensive. This dissertation develops and tests ecient numerical methods for the risk analysis and optimization of large pools of loans. The methods are extensively tested using actual loan data sets. The computational methods proposed here can potentially provide financial institutions and regulators with ecient data-driven methods to manage and estimate risk in large pools of loans.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Management Science and Engineering.
|Glynn, Peter W
|Glynn, Peter W
|Statement of responsibility
|Submitted to the Department of Management Science and Engineering.
|Thesis (Ph.D.)--Stanford University, 2015.
- © 2015 by Justin Sirignano
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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