Citation
Singh, Angad (2021) Mathematical Models of Trading. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/9ks2-fa45. https://resolver.caltech.edu/CaltechTHESIS:09282020-021601265
Abstract
This thesis presents a mathematical framework to model trading of financial assets on an exchange. The interaction between agents on the exchange is modeled as the Nash equilibrium of a demand schedule auction. The submission of demand schedules in the auction is meant to proxy for the submission of limit and market orders on an exchange. Chapter 1 considers this auction in a one-period setting, highlighting the importance of noisy flow for obtaining a unique Nash equilibrium.
Chapter 2 is the core of the thesis and considers the auction in a continuous time setting. Here the agents trading on the exchange have quadratic-type preferences, and in equilibrium they must clear an exogenously specified stream of market orders. Chapter 3 considers alternative and more realistic dynamics for the exogenous market orders. Chapter 4 endogenizes the market orders by considering an agent executing orders on behalf of noisy clients.. Chapter 5 considers the same model as in Chapter 2, except with a consumption based utility function for each agent.
| Item Type: | Thesis (Dissertation (Ph.D.)) | ||||
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| Subject Keywords: | Mathematical Finance, Stochastic Control, Market Microstructure, Optimal Execution, Asset Pricing | ||||
| Degree Grantor: | California Institute of Technology | ||||
| Division: | Physics, Mathematics and Astronomy | ||||
| Major Option: | Mathematics | ||||
| Awards: | Apostol Award for Excellence in Teaching in Mathematics, 2015. | ||||
| Thesis Availability: | Public (worldwide access) | ||||
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| Defense Date: | 17 September 2020 | ||||
| Record Number: | CaltechTHESIS:09282020-021601265 | ||||
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:09282020-021601265 | ||||
| DOI: | 10.7907/9ks2-fa45 | ||||
| ORCID: |
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| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||
| ID Code: | 13969 | ||||
| Collection: | CaltechTHESIS | ||||
| Deposited By: | Angad Singh | ||||
| Deposited On: | 05 Oct 2020 15:39 | ||||
| Last Modified: | 03 Nov 2021 00:02 |
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