A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria
Title | A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria PDF eBook |
Author | Jean-François Chassagneux |
Publisher | American Mathematical Society |
Total Pages | 136 |
Release | 2022-11-10 |
Genre | Mathematics |
ISBN | 1470453754 |
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A Forward-Backward SDEs Approach to Pricing in Carbon Markets
Title | A Forward-Backward SDEs Approach to Pricing in Carbon Markets PDF eBook |
Author | Jean-François Chassagneux |
Publisher | Springer |
Total Pages | 104 |
Release | 2017-10-05 |
Genre | Mathematics |
ISBN | 3319631152 |
In Mathematical Finance, the authors consider a mathematical model for the pricing of emissions permits. The model has particular applicability to the European Union Emissions Trading System (EU ETS) but could also be used to consider the modeling of other cap-and-trade schemes. As a response to the risk of Climate Change, carbon markets are currently being implemented in regions worldwide and already represent more than $30 billion. However, scientific, and particularly mathematical, studies of these carbon markets are needed in order to expose their advantages and shortcomings, as well as allow their most efficient implementation. This Brief reviews mathematical properties such as the existence and uniqueness of solutions for the pricing problem, stability of solutions and their behavior. These fit into the theory of fully coupled forward-backward stochastic differential equations (FBSDEs) with irregular coefficients. The authors present a numerical algorithm to compute the solution to these non-standard FBSDEs. They also carry out a case study of the UK energy market. This involves estimating the parameters to be used in the model using historical data and then solving a pricing problem using the aforementioned numerical algorithm. The Brief is of interest to researchers in stochastic processes and their applications, and environmental and energy economics. Most sections are also accessible to practitioners in the energy sector and climate change policy-makers.
Mean Field Games
Title | Mean Field Games PDF eBook |
Author | François Delarue |
Publisher | American Mathematical Society |
Total Pages | 284 |
Release | 2021-12-14 |
Genre | Mathematics |
ISBN | 1470455862 |
This volume is based on lectures delivered at the 2020 AMS Short Course “Mean Field Games: Agent Based Models to Nash Equilibria,” held January 13–14, 2020, in Denver, Colorado. Mean field game theory offers a robust methodology for studying large systems of interacting rational agents. It has been extraordinarily successful and has continued to develop since its inception. The six chapters that make up this volume provide an overview of the subject, from the foundations of the theory to applications in economics and finance, including computational aspects. The reader will find a pedagogical introduction to the main ingredients, from the forward-backward mean field game system to the master equation. Also included are two detailed chapters on the connection between finite games and mean field games, with a pedestrian description of the different methods available to solve the convergence problem. The volume concludes with two contributions on applications of mean field games and on existing numerical methods, with an opening to machine learning techniques.
Higher Ramanujan Equations and Periods of Abelian Varieties
Title | Higher Ramanujan Equations and Periods of Abelian Varieties PDF eBook |
Author | Tiago J. Fonseca |
Publisher | American Mathematical Society |
Total Pages | 158 |
Release | 2023-01-18 |
Genre | Mathematics |
ISBN | 147046019X |
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Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations
Title | Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations PDF eBook |
Author | Henri Berestycki |
Publisher | American Mathematical Society |
Total Pages | 282 |
Release | 2022-11-10 |
Genre | Mathematics |
ISBN | 1470454297 |
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Planar Algebras in Braided Tensor Categories
Title | Planar Algebras in Braided Tensor Categories PDF eBook |
Author | André Gil Henriques |
Publisher | American Mathematical Society |
Total Pages | 100 |
Release | 2023-02-13 |
Genre | Mathematics |
ISBN | 1470455404 |
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Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows
Title | Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows PDF eBook |
Author | Luchezar Stoyanov |
Publisher | American Mathematical Society |
Total Pages | 134 |
Release | 2023-03-09 |
Genre | Mathematics |
ISBN | 1470456257 |
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