Mathematics Research Projects 2024
Noshin Haque
Advisor: Leslie Cheng
Stock Price Prediction of Netflix
This summer, I want to work on a research project based on predicting stock prices of a company like Netflix, one of the leading companies that is dominating our economy currently. A lot of people use Netflix as their primary source of entertainment: streaming series, movies etc. Therefore, it is possible for us to make large profits by estimating Netflix's stock price. Data Collection and processing would be a significant part of my project. Then I will analyze the stock price data and will be using pricing models such as Multi Period Binomial models and Geometric Brownian Motion to predict stock prices.Throughout the summer, in order to find my solution, I will research several pricing models in further detail.
My initial plan is to review the course materials that I learned in Mathematics of Financial Derivatives. This includes a comprehensive review of topics such as risk management, portfolio theory, and basic pricing models. Additionally, I am eager to delve deeper into advanced pricing models like binomial pricing models, which play a crucial role in accurately forecasting stock prices. I would also learn about softwares that will help me to model stock prices and may use R-Studio to help in visualizing my data through charts and histograms. The stock market is a dynamic, intricate system that is impacted by a wide range of variables, including business performance, industry trends, geopolitical events, and economic indicators. Accurately predicting stock prices has proven to be a challenging task for both researchers and investors.The result of predicting them accurately can lead us to gain profits.
Umme Rafiun Haque
Advisor: Leslie Cheng
Optimal Play in Combinatorial Games
This research delves into the applications of game theory in combinatorial games, aiming to provide a comprehensive understanding of the strategic interactions and decision-making processes within these mathematical models. A combinatorial game is a game with the following characteristics: there are only two players, there are a finite number of moves, it is a zero-sum game (a game that ends with a win for one player and a loss for the other player or a tie/draw for both players), it is deterministic (there are no random moves), and there is perfect information among the players (each player is fully aware of the moves made in the past and their available options from their current position).
The primary goal is to analyze how rational decision-makers interact in combinatorial games, evaluating how their choices, influenced by mutual awareness, impact the outcomes. By studying various combinatorial games in-depth, this project examines the strategies employed by players and the resulting dynamics, offering insights into the patterns and principles that govern strategic behavior.
Furthermore, game theory is vital in the real world as it offers a framework for comprehending strategic interactions among individuals, businesses, and countries, facilitating improved decision-making in competitive scenarios. It aids in predicting and explaining behaviors across various fields, underscoring its significance in economics, politics, and social sciences, and leading to more effective policies and strategies.
Jingxuan (Christine) Yang
Advisor: Leslie Cheng
Modeling the Spread of Influenza in Urban Environments Using Two-Dimensional Random Walk Simulations
As a highly contagious respiratory illness, influenza presents significant public health challenges due to its rapid transmission and seasonal fluctuations. This research aims to explore the patterns of influenza spread in urban environments using random walk models, a statistical tool that represents paths consisting of a series of random steps.
In this project, we will employ two-dimensional random walk simulations to model the spread of influenza in an urban setting. Each individual in the simulation is represented as an agent that moves randomly in a two-dimensional grid, mimicking real-life human movement patterns. We will begin by explaining the theory of the two-dimensional random walk. Subsequently, we will incorporate various factors such as contact rates, population density, and movement patterns derived from real-world data from sources like the CDC and WHO. The significance of this research lies in its potential to enhance our understanding of disease transmission in urban environments, leading to more effective public health interventions