Applications of Stochastic Optimal Control to Pandemic Management, Optimal Energy Production, and Decentralized Finance

Abstract

To demonstrate the flexibility and power of stochastic optimal control theory and the numerical methods therein, this thesis tackles three applied problems which have significant implications in their application fields. The thesis first discusses an optimal control problem in pandemic modeling and mitigation which incorporates novel macroeconomic elements. By modeling the reactions of individuals to current infection levels through personal protective measures which alter disease transmission, improvements in public health outcomes can be achieved with minimal macroeconomic sacrifices. This research was motivated by the 2020 pandemic and presents a tool to aid policymakers in making informed decisions when facing public health crises. Another area that has developed rapidly in recent years is the application of machine learning to problems that would be extremely difficult to solve analytically or with traditional grid-based numerical methods. This thesis extends the literature by developing an efficient and accurate machine learning algorithm to solve the high-dimensional optimal switching problem faced by a power plant operator under uncertain production costs and profits. The algorithm is able to perform accurately on high-dimensional models without suffering from extremely long run times arising from the curse of dimensionality. This could facilitate quicker power plant operator decisions when facing stochastic changes in input factors. Not only does the thesis consider cutting edge technologies for solving stochastic optimization problems, but it also seeks to investigate emerging technologies in financial markets. The thesis combines models of competitive games with empirical data to investigate competition between liquidity providers in a decentralized cryptocurrency exchange. It demonstrates that a Stackelberg game between a mean field of liquidity providers as the leader and a market manipulator as the follower is able to produce extremely accurate predictive results, indicating that the model is accurately capturing pool dynamics and has potential for use in decentralized finance.