| Sumari: | <p>This thesis is a combination of two works using optimal control and imitation learning to address real-world problems in epidemiology and financial markets.</p>
<p>The COVID-19 pandemic has presented unique challenges for policymakers seeking to balance public health and economic impacts. Mathematical models can provide valuable insights to guide lockdown policies. In chapter 1, we propose an extended SIR model incorporating economic decision- making and interactions among susceptible, infected, and recovered populations. An optimal control framework balances infection spread, deaths, and economic activity under lockdown constraints. Experiments high- light trade-offs between short-term recession and long-term benefits. The model provides guidance on lockdown timing, incorporating death costs, and using status information.</p>
<p>In financial markets, historical data provides demonstrations for how ex- pert investors act. Imitation learning offers a data-driven approach to reproduce trading behaviours, without manual reward design needed in reinforcement learning. In chapter 2, we review main imitation learning techniques and applications in finance. Analyses provide error bounds and generalisation guarantees.</p>
<p>The final chapter draws conclusions and list open problems for possible future works.</p>
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