Studies in stochastic optimization and applications
- All machine learning problems reduce to some kind of stochastic optimization problem, which can be solved with variants of algorithms in stochastic approximation literature. In this thesis, we study the classical stochastic optimization algorithms and their extensions to two financial applications. In the first part of this thesis, we revisit the classical stochastic approximation algorithm introduced by Robbins and Monro in 1951, now referred to as the Robbins-Monro procedure. We establish its consistency and utilize the Martingale Central Limit Theorem to prove comprehensive asymptotic normality results for the algorithm. In the second part of this thesis, we introduce a trading algorithm to solve the optimal execution problem in the context of trading in dark pools. The stochastic optimization problem to minimize cost is solved together with an estimation problem to learn the underlying unknown distribution of trading volume limits. Our algorithm solves the two problems which are related, and updates the allocation strategy and the estimations of volume limits alternatively. In the third part of this thesis, we estimate a general non-linear asset pricing model with deep neural network applied to all U.S. equity data combined with a substantial set of macroeconomic and firm-specific information. We include the no-arbitrage condition in the objective and consider a GMM type problem with infinite moment conditions. We combine different neural network structures in a novel way and modify the stochastic optimization algorithms to solve a minimax optimization problem. Our model allows us to understand the key factors that drive asset prices, identify mis-pricing of stocks and generate the mean-variance efficient portfolio.
|Type of resource
|electronic resource; remote; computer; online resource
|1 online resource.
|Degree committee member
|Stanford University, Institute for Computational and Mathematical Engineering.
|Statement of responsibility
|Submitted to the Institute for Computational and Mathematical Engineering.
|Thesis Ph.D. Stanford University 2019.
- © 2019 by Luyang Chen
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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