The principle of least action and stochastic dynamic optimal control — Applications to economic, financial and physical systems

Jussi Lindgren

Research output: ThesisDoctoral ThesisCollection of Articles

Abstract

Economic and financial systems as well as the physical laws of nature can be studied within a common mathematical framework. In particular, the principle of least action and stochastic optimal control can be applied both to resource allocation problems within the society, as well as to derive physical laws. In economic and financial systems, optimal performance is vital, given that economic policies affect all citizens and general welfare. It is also paramount to try to understand the mathematical structure of efficient financial markets. Both these issues are discussed in this Dissertation. First, a stochastic optimal control model is developed to model the dynamics of public debt. In such a dynamical model of public debt, the variance of the debt to GDP ratio is determined in order to assess the risk of insolvency. The model demonstrates also the risks stemming from various feedback mechanisms due to hidden fiscal multipliers and hidden credit risk premia. The model is potentially useful for finance ministries and national debt managers and investors alike. Second, stochastic optimal control is used to derive the key pricing equation from finance theory as an optimality condition for the financial market to be informationally efficient. With such assumptions a nonlinear transport equation is derived for the market instantaneous returns. The model could be used to predict average returns on various assets. Thus the model could be useful for asset managers and investment professionals. Third, it is shown how the key equations of quantum mechanics can also be derived as an optimality condition, when there is background noise stemming from the spacetime fluctuations at small scales. Furthermore, the Heisenberg uncertainty principle is derived from the stochastic optimal control model. Finally, the field equations of electromagnetism are derived from a least action principle and it is shown how Maxwell's equations relate to the Einstein field equation. In particular, the link of electromagnetism and spacetime curvature could be tested empirically in principle and the results could facilitate further engineering applications. The results indicate that strive for efficiency is abundant in natural as well as in economic and financial systems and that the principle of least action is even more omnipresent and important than previously has been known.
Translated title of the contributionPienimmän vaikutuksen periaate ja stokastinen dynaaminen optimisäätö — Sovelluksia talous- ja finanssijärjestelmiin ja fysikaalisiin systeemeihin
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
Supervisors/Advisors
  • Salo, Ahti, Supervising Professor
  • Liukkonen, Jukka, Thesis Advisor, External person
  • Salo, Ahti, Thesis Advisor
Publisher
Print ISBNs978-952-64-0537-7
Electronic ISBNs978-952-64-0538-4
Publication statusPublished - 2021
MoE publication typeG5 Doctoral dissertation (article)

Keywords

  • principle of least action
  • stochastic optimal control
  • public finance
  • derivatives pricing
  • quantum mechanics
  • general relativity

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