### Browsing by Author "Salo, Ahti, Prof., Aalto University, Finland"

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Item The principle of least action and stochastic dynamic optimal control — Applications to economic, financial and physical systems(Aalto University, 2021) Lindgren, Jussi; Liukkonen, Jukka, Dr., Radiation and Nuclear Safety Authority, Finland; Salo, Ahti, Prof., Aalto University, Finland; Matematiikan ja systeemianalyysin laitos; Department of Mathematics and Systems Analysis; Perustieteiden korkeakoulu; School of Science; Salo, Ahti, Prof., Aalto University, Department of Mathematics and Systems Analysis, FinlandEconomic 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.Item Rank-based information in multi-attribute decision and efficiency analysis(Aalto University, 2012) Punkka, Antti; Salo, Ahti, Prof., Aalto University, Finland; Matematiikan ja systeemianalyysin laitos; Department of Mathematics and Systems Analysis; Systems Analysis Laboratory; Perustieteiden korkeakoulu; School of Science; Salo, Ahti, Prof., Aalto University, FinlandAdditive multi-attribute value models are widely employed in decision and efficiency analysis. Difficulties in specifying preferences for these models have motivated the development of methods that admit incomplete preference information, identify non-dominated alternatives and provide recommendations with heuristic decision rules. These methods accommodate many types of preference statements. Yet, several studies suggest that decision makers prefer to provide rank-based information rather than numerical statements. First, this thesis defines the notion of incomplete ordinal information, which can capture statements about the relative importance of the attributes and about the achievement levels of alternatives. The thesis then develops an optimization model for identifying non-dominated alternatives when alternatives and preferences are characterized by incomplete ordinal information and possibly by other types of incomplete information. These forms of information can, for example, help stakeholders to arrive at a joint preference characterization. Second, the thesis shows that the recommendations of many decision rules depend on the selected normalization of value functions. Motivated partly by this, the thesis develops optimization models to determine all the rankings the alternatives attain with the model parameters that are consistent with the stated incomplete information. The resulting ranking intervals help, for example, analyze how sensitive the alternatives' rankings are to the model parameters. Third, the thesis introduces dominance relations and ranking intervals for the efficiency analysis of decision making units when efficiency is measured through ratios of multi-attribute output and input values, as in the original data envelopment analysis method. These relations and intervals, which can be computed with the optimization models developed in the thesis, make it possible to compare any two decision making units independent of what other units are included in the analysis and to analyze how sensitive the efficiency of a unit is to the output and input attribute weights.