Related papers: Entropy-Maximizing Dynamics of Continuous Markets

We obtain estimates on the exponential rate of decay of the relative entropy from equilibrium for Markov processes with a non-local infinitesimal generator. We adapt some of the ideas coming from the Bakry-Emery approach to this setting. In…

Covariate balance is a conventional key diagnostic for methods used estimating causal effects from observational studies. Recently, there is an emerging interest in directly incorporating covariate balance in the estimation. We study a…

Group Relative Policy Optimization (GRPO) has emerged as a promising approach for improving the reasoning capabilities of large language models. However, it struggles to effectively balance the tradeoff between exploration and exploitation…

This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…

We propose a thermodynamically motivated measure of gravitational entropy based on the Bel-Robinson tensor, which has a natural interpretation as the effective super-energy-momentum tensor of free gravitational fields. The specific form of…

We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving…

This paper studies a continuous-time optimal portfolio selection problem in the complete market for a behavioral investor whose preference is of the prospect type with probability distortion. The investor concerns about the terminal…

We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal…

Reinforcement learning (RL) has become a powerful paradigm for optimizing large language models (LLMs) to handle complex reasoning tasks. A core challenge in this process lies in managing policy entropy, which reflects the balance between…

In view of the recent quest for well-behaved nonlinear extensions of the traditional Schroedinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the…

This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…

The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…

The paper predicts an Efficient Market Property for the equity market, where stocks, when denominated in units of the growth optimal portfolio (GP), have zero instantaneous expected returns. Well-diversified equity portfolios are shown to…

We propose a scalable, policy-centric framework for continuous-time multi-asset portfolio-consumption optimization under inequality constraints. Our method integrates neural policies with Pontryagin's Maximum Principle (PMP) and enforces…

The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…

Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…

A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the…

We focus on the study of dynamics of two kinds of random walk: generic random walk (GRW) and maximal entropy random walk (MERW) on two model networks: Cayley trees and ladder graphs. The stationary probability distribution for MERW is given…

We consider an investor who is dynamically informed about the future evolution of one of the independent Brownian motions driving a stock's price fluctuations. With linear temporary price impact the resulting optimal investment problem with…

We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed…