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Mathematical Models of Trading


Singh, Angad (2021) Mathematical Models of Trading. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/9ks2-fa45.


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.))
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)
Research Advisor(s):
  • Cvitanić, Jakša
Thesis Committee:
  • Tamuz, Omer (chair)
  • Cvitanić, Jakša
  • Jin, Lawrence Jiaqi
  • Katz, Nets H.
Defense Date:17 September 2020
Record Number:CaltechTHESIS:09282020-021601265
Persistent URL:
Singh, Angad0000-0001-6677-7013
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13969
Deposited By: Angad Singh
Deposited On:05 Oct 2020 15:39
Last Modified:03 Nov 2021 00:02

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