Application of optimal control theory to firm financing and investment

Abstract

In modern society, one can notice the tendency to optimize every action that can be measured with a valuable unit. For instance, in economics, the unlimited demand has to be satisfied with limited supply, while in finance an unlimited number of investment opportunities arise for a finite amount of funds. One shouldn’t base certain allocation decisions purely on intuition or made-up signals as it would turn every economy and firm into a large gambling game. This dissertation aims to determine how allocation processes, specifically sequential investments, firm financing, price forecasting, and algorithmic trading, can be optimized based on certain mathematical techniques found in Optimal Control theory. The results obtained show that optimization can indeed happen, with the establishment of a switching point for a company to change its pay-out policy, various simulations for the prediction of crude oil prices, a systematic process on how to identify the optimal allocation in sequential investments, and the use of optimal filtering for algorithmic trading signals. To visualize the above results, the dissertation was structured so that the reader can comprehend the logic of optimal control theory prior to any application.