The research question
A forecast of tomorrow’s return can be viewed as a probability distribution rather than a single value. My thesis investigated how ideas from data-driven optimal transport could inform that distribution, and how dynamic programming could connect a forecast to a sequence of decisions.
The mathematical approach
The work draws on the distributional barycenter problem and data-driven flows. It considers conditional density estimation, transport maps, and numerical methods for relating observed samples to an unknown distribution.
The thesis builds on work by Esteban G. Tabak, Giulio Trigila, and Wenjun Zhao. It describes a formulation that replaces a more difficult minimax optimization with a single minimization, and investigates how the approach might be applied to financial time series.
Financial setting and scope
The thesis includes descriptive analysis and density-estimation experiments using Apple, Tesla, Google, and Amazon price data collected through Tiingo. Conditional density estimation and much of the forecasting application remained future work; the trading section sketches decision rules rather than a completed dynamic-programming solution.
This is an academic record of an exploratory project, with the original PDF and a separate errata note available below. It does not establish a validated trading strategy or a claim of investment outperformance.
Explore the geometry.
This small interactive example shows how probability mass moves between two one-dimensional Gaussian distributions.