Defence of doctoral thesis in the field of Systems and Operations Research, M.Soc.Sc. Jussi Lindgren

The aim of stochastic optimal control is to optimize systems over time when the dynamics is perturbed by external noise. The models developed in this dissertation demonstrate how stochastic optimal control can be applied to modeling and controlling economic systems, as well to describe physics laws.

The overarching theme of the dissertation is the principle of least action and optimal control of systems. The principle of least action was developed already in the 18th century in the context of analytical mechanics. It is also useful in systems theory, as optimal control theory can be seen as a generalization of calculus of variations; achieving given objectives with least costs.

In the dissertation it is demonstrated how the dynamics of public debt can be nonlinear even with mild assumptions and it is demonstrated how the political decision-maker should conduct economic policy, when there are uncertainties present as regards the rate of interest and economic growth. The results are relevant in terms of managing the risks related to government debt. The results can provide support for rational economic policy-making as well.

The dissertation builds also a new model for operationalizing the efficient markets hypothesis. In efficient markets, the financial market minimizes information-related costs over time. The stochastic control problem is directly related to pricing of financial derivatives, as the optimality condition in its linearized form is the Black-Scholes partial differential equation. The model derived for the instantaneous returns could be useful for asset managers and algorithmic trading.

The dissertation also shows how fundamental laws of quantum mechanics can be understood from the point of view of stochastic optimal control. It becomes evident that relativistic equations of quantum mechanics can be understood through an interpretation, where the spacetime itself is fluctuating at small scales. The Heisenberg uncertainty principle is thus interpreted in a new way and it is derived from the model assumptions. In addition, it is shown how the principle of least action, classical electromagnetism and general theory of relativity can be understood together in the same context. The results could facilitate further fundamental research in theoretical physics and in the philosophy of science related to theoretical physics.

Opponent is Professor Grigorios A. Pavliotis, Imperial College London, UK

Custos is Professor Ahti Salo, Aalto University School of Science, Department of Mathematics and Systems Analysis

Contact details of the doctoral student: [email protected]

The public defence will be organised via Zoom and on campus. Link to the event

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The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic thesis (will be added)