Related papers: Shifted Brownian Fluctuation Game
We consider fractional Brownian motion with the Hurst parameters from (1/2,1). We found that the increment of a fractional Brownian motion can be represented as the sum of a two independent Gaussian processes one of which is smooth in the…
A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility. We investigate the interplay between correlation coefficients and Hurst exponents and propose a novel…
Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and…
Optimal execution in financial markets refers to the process of strategically transacting a large volume of assets over a period to achieve the best possible outcome by balancing the trade-off between market impact costs and timing or…
Trading frictions are stochastic. They are, moreover, in many instances fast-mean reverting. Here, we study how to optimally trade in a market with stochastic price impact and study approximations to the resulting optimal control problem…
Collisional Brownian engines have attracted significant attention due to their simplicity, experimental accessibility, and amenability to exact analytical solutions. While previous research has predominantly focused on optimizing mean…
The movement of a Brownian particle in a fluctuating two-state periodic potential is investigated. At high transition rate, we use a perturbation method to obtain the analytical solution of the model. It is found that the net current is a…
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 consider an insurance entity endowed with an initial capital and a surplus process modelled as a Brownian motion with drift. It is assumed that the company seeks to maximise the cumulated value of expected discounted dividends, which are…
Dynamics of information flow in adaptively interacting stochastic processes is studied. We give an extended form of game dynamics for Markovian processes and study its behavior to observe information flow through the system. Examples of the…
Market participants regularly send bid and ask quotes to exchange-operated limit order books. This creates an optimization challenge where their potential profit is determined by their quoted price and how often their orders are…
The scope of this paper is to study the optimal stopping problems associated to a stochastic process, which may represent the gain of an investment, for which information on the final value is available a priori. This information may…
Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…
In the last two decades, fluctuation theorems have been proved formally and demonstrated experimentally for several variables (such as entropy production, work, or flux) and different noises causing the fluctuations (of either thermal or…
In this work, we propose two models of coupled harmonic oscillators under Brownian motion to computationally study the applications of fluctuation theorems. This paper also illustrates how to analytically calculate free energy differences…
This work uses game theory as a mathematical framework to address interaction modeling in multi-agent motion forecasting and control. Despite its interpretability, applying game theory to real-world robotics, like automated driving, faces…
Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…
We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…
In this paper we discuss the process convergence of the time dependent fluctuations of linear eigenvalue statistics of random circulant matrices with independent Brownian motion entries, as the dimension of the matrix tends to $\infty $.…
Recent results on the stationary state Fluctuation Theorems for work and heat fluctuations of Langevin systems are presented. The relevance of finite time corrections in understanding experimental and simulation results is explained in the…