Publications de Max-Olivier Hongler

Nonlinear Economic State Equilibria via van der Waals Modeling

The renowned van der Waals (VDW) state equation quantifies the equilibrium relationship between the pressure P, volume V, and temperature (Formula presented.) of a real gas. We assign new variable interpretations adapted to the economic context: (Formula p ...

2024

Stochastic pairwise preference convergence in Bayesian agents

Max-Olivier Hongler

Beliefs inform the behaviour of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack critical theory to ...

2024

AN EXACT BANDIT MODEL FOR THE RISK-VOLATILITY TRADEOFF

Max-Olivier Hongler

. We revisit the two-armed bandit (TAB) problem where both arms are driven by diffusive stochastic processes with a common instantaneous reward. We focus on situations where the Radon-Nikodym derivative between the transition probability densities of the f ...

Springfield2024

Can one hear the shape of a target zone?

Max-Olivier Hongler

We develop an exchange rate target zone model with finite exit time and non-Gaussian tails. We show how the tails are a consequence of time-varying investor risk aversion, which generates mean-preserving spreads in the fundamental distribution. We solve ex ...

2023

Opinion formation dynamics - Swift collective disillusionment triggered by unmet expectations

Max-Olivier Hongler

We propose a microscopic model to describe how individual opinions shared between interacting agents initiate excessive collective expectations about a new idea or an innovation, followed by a swift collapse towards a dramatic collective disillusionment. T ...

2021

Cauchy Processes, Dissipative Benjamin–Ono Dynamics and Fat-Tail Decaying Solitons

Max-Olivier Hongler

In this paper, a dissipative version of the Benjamin–Ono dynamics is shown to faithfully model the collective evolution of swarms of scalar Cauchy stochastic agents obeying a follow-the-leader interaction rule. Due to the Hilbert transform, the swarm dynam ...

2021

How Chaotic Dynamics Drive a Vintage Grill-Room Spit

Max-Olivier Hongler

In 1943 Yves Rocard published an amazing book entitled "Dynamique Generale des Vibrations". Among a collection of mechanical devices that are studied with great care in the book, the so-called Bouasse-Sarda's "tournebroche" (rotary grill spit) is a fascina ...

Springer Nature2021

Increasing risk: Dynamic mean-preserving spreads

Max-Olivier Hongler

We extend the celebrated Rothschild and Stiglitz (1970) definition of Mean-Preserving Spreads to a dynamic framework. We adapt the original integral conditions to transition probability densities, and give sufficient conditions for their satisfaction. We t ...

2020

Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

Max-Olivier Hongler

he concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose ...

2020

Mean-Field Games And Swarms Dynamics In Gaussian And Non-Gaussian Environments

Max-Olivier Hongler

The collective behaviour of stochastic multi-agents swarms driven by Gaussian and non-Gaussian environments is analytically discussed in a mean-field approach. We first exogenously implement long range mutual interactions rules with strengths that are weig ...

AMER INST MATHEMATICAL SCIENCES-AIMS2020

Imitation, Proximity, and Growth - A Collective Swarm Dynamics Approach

Max-Olivier Hongler, Fariba Hashemi, Olivier Gallay

This paper is based on the premise that economic growth is driven by an interplay between innovation and imitation in an economy composed of interacting ̄rms operating in a stochastic environment. A novel approach to modeling imitation is presented based o ...

2019

On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications

Max-Olivier Hongler, Roger Filliger

We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial dif ...

Springer2019

Unraveling Brittle-Fracture Statistics from Intermittent Patterns Formed During Femtosecond Laser Exposure

Max-Olivier Hongler, Yves Bellouard, Christos Edouardos Athanasiou

Femtosecond-laser-written patterns at the surface of brittle materials may show at random times spontaneous alternations from regular to disordered structures and vice versa. Here, we show that these random transitions carry relevant statistical informatio ...

American Physical Society (APS)2017

Intearcting Brownian Swarms: Some Analytical Results

Max-Olivier Hongler, Guillaume Adrien Sartoretti

We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances ...

MDPI AG2016

Exact soliton-like probability measures for interacting jump processes

Max-Olivier Hongler

The cooperative dynamics of a 1-D collection of Markov jump, interacting stochastic processes is studied via a mean-field (MF) approach. In the time-asymptotic regime, the resulting nonlinear master equation is analytically solved. The nonlinearity compens ...

2015

Decentralized Self-Selection of Swarm Trajectories: From Dynamical Systems to Robotic Implementation

Francesco Mondada, Max-Olivier Hongler, Guillaume Adrien Sartoretti, Marcelo Elias de Oliveira

In this paper, we present a distributed control strategy, enabling agents to converge onto and travel along a consensually selected curve among a class of closed planar curves. Individual agents identify the number of neighbors within a finite circular sen ...

Springer Verlag2014

The estimation problem and heterogenous swarms of autonomous agents

Max-Olivier Hongler, Guillaume Adrien Sartoretti

2014

Local versus nonlocal barycenttic interactions in 1 D agent dynamics

Max-Olivier Hongler, Olivier Gallay, Roger Filliger

The mean-field dynamics of a collection of stochastic agents evolving under local and nonlocal interactions in one dimension is studied via analytically solvable models. The nonlocal interactions between agents result from (a) a finite extension of the age ...

Amer Inst Mathematical Sciences2014

Self-Organized Mixed Canonic-Disipative Dynamics for Brownian Planar Agents

Max-Olivier Hongler, Guillaume Adrien Sartoretti

2013

Super-Diffusive Noise Source in Asset Dynamics

Max-Olivier Hongler

2013