This thesis examines the progression of portfolio optimization techniques from traditional (Markowitz and CAPM) to much more computationally advanced techniques such as Machine Learning and LLMs. Using a 15 year dataset of daily S&P500 returns, we show that Long Short-Term Memory (LSTMs) excel at capturing much shorter-term return forecasting compared to Deep Neural Networks (DNNs) which excel at discerning complex, otherwise invisible patterns in the long term and map straight from input data to asset weights. Both approaches surpass classical benchmarks in risk-adjusted performance. Lastly, we introduce a Large Language Model (LLM)–based simulator, demonstrating how ChatGPT can effectively synthesize (e.g., news headline sentiment, policy announcements) into allocation decisions. Our findings highlight the promising future of prompt engineering as well as LLM’s promising ability to combine numerical and textual insight into, potentially, better understood portfolio strategies.

This thesis develops a multi–period portfolio optimization framework that integrates short–term alpha signals with practical trading constraints, including market impact and deviation risk. By transforming the problem from portfolio–space variables to impact–space variables, our model captures the primary trade–off between harnessing alpha and mitigating market impact, while a risk penalty is imposed to ensure adherence to a target portfolio. After deriving the foundational objective function, the framework is enhanced through the incorporation of multiple alpha signals with distinct decay profiles and Monte Carlo simulations to account for forecast uncertainty. Comprehensive performance evaluations are conducted using an array of benchmarks—including linear trading, all–at–once execution, and half–at–midpoint trading—across metrics such as final wealth, cumulative return, volatility, maximum drawdown, turnover, tracking error, and implementation shortfall. The approach is further extended to multi–asset portfolios, where outcomes are compared across varying levels of stock correlation. Our results demonstrate that, despite the optimized trade schedule often resembling a nearly linear strategy, subtle deviations to exploit alpha allow for meaningful improvements in risk–adjusted performance. This work contributes both theoretical insights and practical tools for managing portfolio transitions in the presence of realistic market frictions and dynamic return forecasts, offering a pathway for future research into more complex cross–asset dynamics and nonlinear impact functions.

This thesis investigates interest rate hedging strategies for mitigating financial risks in reverse mortgage portfolios. Reverse mortgages are impacted by a complex interplay of interest rate volatility, borrower longevity, and housing price fluctuations. Using a two-pronged approach combining theoretical Monte Carlo simulations and empirical analysis of Ginnie Mae HECM loan data, the study evaluate the effectiveness of various hedging instruments, with particular emphasis on interest rate swaps. The simulation model applies a NNEG (No-Negative-Equity Guarantee) framework to conduct a sensitivity analysis on reverse mortgage risk factors. While theoretical models suggests an optimized barbell hedging strategy could have high hedge effectiveness (87-93%), Ginnie Mae data shows a dramatically lower effectiveness. This divergence between theory and practice highlights how diversified hedging approaches with portfolio segmentation might be more effective than traditional duration-matching techniques. The findings contribute to a realistic and theoretical understanding of reverse mortgage risk management, with implications to how lenders can minimize the burden of their risk in a increasingly popular retirement financing market.

Recent developments and popularity in prediction markets, in addition to the increase in recent advertisements of sports gambling, have been very prevalent throughout 2024 and the early months of 2025. In an effort to explore whether or not these spaces could offer consistent profit comparable to other investment techniques, excluding arbitrage opportunities, this work attempts to measure the profitability of NBA sports book wagers by developing a data-driven machine learning model that measures the true probability of an NBA team winning a game on a specific night. This work is novel, in that it places greater emphasis on exploring the relationship that moneyline odds have with game outcomes. First, we perform feature engineering to expand our initial dataset, which contains historical moneyline odds alongside game outcomes, into a multitude of components that are associated with the home team's win rate. We then train our model with data of the first 41 games that each of the 30 NBA teams played in a given season, and utilize machine learning algorithms to predict the true probability a team has of winning a game. This is then compared to the implied probabilities sports book set, which is derived from their listed moneyline odds, to provide novel insights. While the algorithms achieve an average accuracy of 70%, the insight gained from attempting to measure profitability in the first half of the 2022-23 NBA season ultimately lays computational and methodological foundations for analyzing associations with moneyline odds.