Finalist Award in the 2022 MCM

• Full paper: Greedy Prophet: Make You the Next Oracle of Omaha

• Certificate of Achievement: Finalist Award in the 2022 Mathematical Contest In Modeling

Problem Statement

The 2022 MCM problems represented a variety of challenging problems spanning the familiar to the new. Each problem required teams to apply unique mathematical modeling skills to answer the questions posed. All three problems were created by the MCM Problem Committee, a unique blend of academicians and industry professionals with many years of mathematical modeling experience. Teams had to be at the top of their game to excel.

For the C problem, teams were presented with a forecasting and allocation optimization problem from a market trader perspective. Students were presented with five years of data on gold and bitcoin prices and were required to develop strategies on how to trade an initial $1000 stake using only the data provided and only up to the date of each trade. Complicating the analysis, the problem charged substantial commissions for each trade. Teams were required to justify why their approach was the best approach - a very challenging task for them. The official problem statement can be found in this document.

Our Work

The whole structure of our work is represented in Figure 1. To solve the proposed portfolio selection problem, we first investigated the data, pre-processed the missing value, and extracted some basic properties of daily prices from 9/11/2016 to 9/10/2021. Then, we calculated the price volatility of gold and bitcoin, the price correlation between gold and bitcoin, and the return correlation between gold and bitcoin to find suitable models.

Next, we developed the model “greedy prophet” for online portfolio selection. The whole model can be decomposed into two parts: the prediction model and the decision model. In the prediction model, we used the moving average approach in the first year since data is not enough for training machine learning models. Then, from the second year till the end, we proposed an ensemble model that integrates XGBoost, LightGBM, and KNN. Metrics show that the ensemble model has better performance than single ones and outputs satisfying results with high accuracy. As to the decision model, the “greedy policy” was applied. We formulated a mathematical optimization problem to maximize the predicted net profit of the next day. After transformation, this problem can be easily solved and output daily trading strategies.

After that, we proved the optimality of our “greedy prophet” by comparing the ultimate wealth given by five other models. Sensitivity to transaction costs is analyzed under different combinations of commissions of gold and bitcoin. After that, the strengths and weaknesses of our model are listed and further improvements are also discussed. At last, we design a memorandum to introduce the model and show the best strategy and corresponding results to the trader.