相关论文: A duality approach to a price formation MFG model

We consider Cournot mean field games of controls, a model originally developed for the production of an exhaustible resource by a continuum of producers. We prove uniqueness of the solution under general assumptions on the price function.…

We establish a probabilistic framework for analysing extended mean-field games with multi-dimensional singular controls and state-dependent jump dynamics and costs. Two key challenges arise when analysing such games: the state dynamics may…

We investigate the mean-field limit for interacting particle systems through a duality-based framework and obtain quantitative estimates on the convergence of marginals as well as on correlation functions. In particular, for merely…

The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative…

In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of…

Traditional electric energy markets do not explicitly model generator contingencies. To improve the representation of resources and to enhance the modeling of uncertainty, existing markets are moving in the direction of including generator…

Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…

We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of…

We consider the pricing problem facing a seller of a contingent claim. We assume that this seller has some general level of partial information, and that he is not allowed to sell short in certain assets. This pricing problem, which is our…

The duality principle in option pricing aims at simplifying valuation problems that depend on several variables by associating them to the corresponding dual option pricing problem. Here, we analyze the duality principle for options that…

We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…

We develop a theory of bid and ask price dynamics where the two prices form due to interaction of buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask"…

We study mean-field game (MFG) problems with rough common noise, in which the representative state dynamics are governed by a controlled rough stochastic differential equation driven by an idiosyncratic Brownian motion and a deterministic…

Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…

In a game theoretic framework, we study energy markets with a continuum of homogenous producers who produce energy from an exhaustible resource such as oil. Each producer simultaneously optimizes production rate that drives her revenues, as…

Our aim is to model a game for power as a dynamical process, where an excess of power possessed by a player allows him to gain even more power. Such a positive feedback is often termed as the Matthew effect. Analytical and numerical methods…

While the general theory for the terminal-initial value problem in mean-field games is widely used in many models of applied mathematics, the modeling potential of the corresponding forward-forward version is still under-considered. In this…

This paper studies the mean field game (MFG) problem arising from a large population competition in fund management, featuring a new type of relative performance via the benchmark tracking. In the $n$-player model, each agent aims to…

The second order Mean Field Games system (MFGS) in a bounded domain with the lateral Cauchy data is considered. This means that both Dirichlet and Neumann boundary data for the solution the MFGS are given. Two H\"older stability estimates…

Finite-state mean-field games (MFGs) arise as limits of large interacting particle systems and are governed by an MFG system, a coupled forward-backward differential equation consisting of a forward Kolmogorov-Fokker-Planck (KFP) equation…