Adaptive robust control with statistical learning

Thesis

In stochastic control problems the agent chooses the optimal strategy to maximise or minimise the performance criterion. The performance criterion can be either the expectation of a reward function for the standard control problem or the non-linear expectation for the robust control problem. In parameterised stochastic control problems, the agent needs to know the value of the model parameters in the stochastic system to specify the optimal strategy correctly. However, it is hardly the case that the agent knows the values of the model parameters.

In this thesis, we aim to study a robust stochastic control problem where the agent does not know the values of the parameters of the underlying process. Therefore, we frame the stochastic control problem where we assume that the agent does not know the values of the model parameters. However, the agent uses the observable processes to estimate the values of the model parameters while simultaneously solving the stochastic control problem in a robust framework.

There are two key components in this new stochastic control problem. The first component is the parameter estimation part where the agent uses the realisation of the underlying process to estimate the unknown parameters in the stochastic system. We particularly focus on online parameter estimation. The online estimator is an important ingredient for our stochastic control problem because this type of estimator allows the agent to obtain the optimal strategy in feedback form. The second component is the stochastic control part which is the question of how to design a time-consistent stochastic control problem that allows the agent to also estimate the parameters and optimise her strategy simultaneously. In this thesis, we address each component of the problem above in the continuous-time setting and then the utility maximisation problem under this framework is studied carefully.

Authors: Bhudisaksang, T

• DOI: 10.5287/ora-o8yynnyyr
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: stochastic gradient descent; algorithmic trading; statistical learning; stochastic control; model uncertainty
• Subjects: financial mathematics; statistics