Related papers: Iterated Function Systems with Economic Applicatio…

This article discusses the application of stochastic intervention to find the optimal treatment distribution yielding a high value of expected potential outcome under the setting where the number of treatments is allowed to vary with $n$.…

This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of…

We consider an infinite dimensional optimization problem motivated by mathematical economics. Within the celebrated "Arbitrage Pricing Model", we use probabilistic and functional analytic techniques to show the existence of optimal…

We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…

Ergodicity economics is a new branch of economic theory that notes the conceptual difference between time averages and expectation values, which coincide only for ergodic observables. It postulates that individual agents maximise the time…

Autonomous mechanisms have been proposed to regulate certain aspects of society and are already being used to regulate business organisations. We take seriously recent proposals for algorithmic regulation of society, and we identify the…

When the experimental objective is expressed by a set of estimable functions, and any eigenvalue-based optimality criterion is selected, we prove the equivalence of the recently introduced weighted optimality and the 'standard' optimality…

Evolutionary Algorithms are naturally inspired approximation optimisation algorithms that usually interfere with science problems when common mathematical methods are unable to provide a good solution or finding the exact solution requires…

We focus on how individual behavior that complies with social norms interferes with performance-based incentive mechanisms in organizations with multiple distributed decision-making agents. We model social norms to emerge from interactions…

In recent years, we have observed a significant trend towards filling the gap between social network analysis and control. This trend was enabled by the introduction of new mathematical models describing dynamics of social groups, the…

Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual…

We propose and study a system whose dynamics are governed by predictions of its future states. General formalism and concrete examples are presented. We find that the dynamical characteristics depend on both how to shape predictions as well…

A model among many may only be best under certain states of the world. Switching from a model to another can also be costly. Finding a procedure to dynamically choose a model in these circumstances requires to solve a complex estimation…

In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general time-varying random demand. Our main goal is to study the optimal policies, which can be…

The sum-utility maximization problem is known to be important in the energy systems literature. The conventional assumption to address this problem is that the utility is concave. But for some key applications, such an assumption is not…

This thesis is devoted to the study of dynamical properties of diluted models. These are mean field statistical mechanics systems, but with finite local connectivity. Among other reasons, the interest for these models arises from their deep…

We consider a problem of optimal investment with intermediate consumption and random endowment in an incomplete semimartingale model of a financial market. We establish the key assertions of the utility maximization theory assuming that…

Many systems are partially stochastic in nature. We have derived data driven approaches for extracting stochastic state machines (Markov models) directly from observed data. This chapter provides an overview of our approach with numerous…

We demonstrate by mathematical analysis and systematic computer simulations that redistribution can lead to sustainable growth in a society. The human capital dynamics of each agent is described by a stochastic multiplicative process which,…

Optimization is widely used for decision making across various domains, valued for its ability to improve efficiency. However, poor implementation practices can lead to unintended consequences, particularly in socioeconomic contexts where…