Equilibrium Theory: A Simple Production Model

2019 ◽  
pp. 451-457
Author(s):  
Tomas Björk
Keyword(s):  
Equilibrium Problem ◽  
Optimization Problem ◽  
Dynamic Equilibrium ◽  
Equilibrium Theory ◽  
Production Model ◽  
Stochastic Discount Factor ◽  
Equilibrium Concept ◽  
Precise Formulation ◽  
Central Planner ◽  
Simple Production

This is the first of several chapters dealing with the dynamic equilibrium theory. As an instructive first example we study a simple Cox–Ingersoll–Ross type of production model. The equilibrium concept is given a precise formulation and we derive the equilibrium short rate as well as the equilibrium stochastic discount factor. We also study the associated optimization problem for a central planner and prove that this is equivalent to the equilibrium problem.

Arbitrage Theory in Continuous Time

2019 ◽  
Author(s):  
Tomas Björk
Keyword(s):  
Incomplete Markets ◽  
Continuous Time ◽  
Dynamic Equilibrium ◽  
Factor Model ◽  
Good Deal ◽  
Financial Derivatives ◽  
Equilibrium Theory ◽  
Martingale Measure ◽  
Fourth Edition ◽  
Optimal Stopping Theory

The fourth edition of this textbook on pricing and hedging of financial derivatives, now also including dynamic equilibrium theory, continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous time arbitrage pricing of financial derivatives, including stochastic optimal control theory and optimal stopping theory, the book is designed for graduate students in economics and mathematics, and combines the necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. All concepts and ideas are discussed, not only from a mathematics point of view, but the mathematical theory is also always supplemented with lots of intuitive economic arguments. In the substantially extended fourth edition Tomas Björk has added completely new chapters on incomplete markets, treating such topics as the Esscher transform, the minimal martingale measure, f-divergences, optimal investment theory for incomplete markets, and good deal bounds. There is also an entirely new part of the book presenting dynamic equilibrium theory. This includes several chapters on unit net supply endowments models, and the Cox–Ingersoll–Ross equilibrium factor model (including the CIR equilibrium interest rate model). Providing two full treatments of arbitrage theory—the classical delta hedging approach and the modern martingale approach—the book is written in such a way that these approaches can be studied independently of each other, thus providing the less mathematically oriented reader with a self-contained introduction to arbitrage theory and equilibrium theory, while at the same time allowing the more advanced student to see the full theory in action.

Modeling of Interannual Snow and Ice Storage in High-Altitude Regions by Dynamic Equilibrium Concept

2014 ◽  
Vol 19 (12) ◽  
pp. 04014034 ◽  
Author(s):  
Noriaki Ohara ◽  
SuHyung Jang ◽  
Shuichi Kure ◽  
Z. Q. Richard Chen ◽  
M. Levent Kavvas
Keyword(s):  
High Altitude ◽  
Dynamic Equilibrium ◽  
Ice Storage ◽  
Equilibrium Concept ◽  
Snow And Ice

scholarly journals Split equality common null point problem for Bregman quasi-nonexpansive mappings

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3917-3932
Author(s):  
Ali Abkar ◽  
Elahe Shahrosvand
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Banach Spaces ◽  
Optimization Problem ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Fixed Point Problem ◽  
Null Point ◽  
Point Problem ◽  
Reflexive Banach Spaces

In this paper, we introduce a new algorithm for solving the split equality common null point problem and the equality fixed point problem for an infinite family of Bregman quasi-nonexpansive mappings in reflexive Banach spaces. We then apply this algorithm to the equality equilibrium problem and the split equality optimization problem. In this way, we improve and generalize the results of Takahashi and Yao [22], Byrne et al [9], Dong et al [11], and Sitthithakerngkiet et al [21].

scholarly journals Advanced results on variational inequality formulation in oligopolistic market equilibrium problem

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 935-947 ◽  
Author(s):  
Annamaria Barbagallo
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Lipschitz Continuity ◽  
Dynamic Equilibrium ◽  
Market Equilibrium ◽  
Equilibrium Solutions ◽  
Evolutionary Variational Inequality ◽  
Oligopolistic Market ◽  
Continuity Result ◽  
Discretization Procedure

The aim of the paper is to study the regularity of the solution to the evolutionary variational inequality governing the dynamic oligopolistic market equilibrium problem in presence of production excesses. More precisely, we obtain a Lipschitz continuity result with respect to time for such a solution. Moreover, we introduce a discretization procedure for computing dynamic equilibrium solutions and we provide a numerical example.

Appalachian Peneplains: An Historical Review

1983 ◽  
Vol 2 (2) ◽  
pp. 156-164 ◽  
Author(s):  
William Sevon ◽  
Noel Potter ◽  
George Crowl
Keyword(s):  
Early Identification ◽  
Dynamic Equilibrium ◽  
Historical Review ◽  
Mineral Resources ◽  
Equilibrium Concept ◽  
Long Period ◽  
Surficial Deposits ◽  
Relationship Of ◽  
The Relationship ◽  
Evolutionary Progression

The concept that erosion, over a long period of time, would produce an evolutionary progression of landforms culminating in a nearly flat plain, the peneplain, was formulated into a coherent theory by W. M. Davis. Subsequent to early identification of the Fall Zone (oldest), Schooley, Harrisburg, and Somerville (youngest) peneplains, numerous workers pursued identification, correlation, description, folding, formative processes, and dating of Appalachian peneplains for 6 decades. Following a peak of interest and activity in the 1930's, work on Appalachian peneplains declined rapidly. Reasons for the decline include: death of former workers, diversion into other lines of research, and rise of process geomorphology. Phenomena attributed to a dependence on peneplanation include: origin of present drainage, origin of some mineral resources, and cementation of rock units. Attacks on the peneplain idea have been largely unsuccessful except for the dynamic equilibrium concept advocated by John Hack. Controversy exists about whether the disparity between rates of uplift and denundation allow adequate time for peneplanation to occur. The relationship of some surficial deposits to presumed peneplain surfaces is problematical. The peneplain concept is still alive, but new lines of research are required to resolve its controversial position.

Structural Topology Design Optimization for Controlled Crash Behavior

2003 ◽  
Author(s):  
Ciro A. Soto
Keyword(s):  
Design Optimization ◽  
Automotive Industry ◽  
Optimization Problem ◽  
Dynamic Equilibrium ◽  
Topology Design ◽  
Structural Behavior ◽  
Structural Topology ◽  
Design Engineers ◽  
Optimum Topology ◽  
Structural Topology Design

This paper presents a methodology to perform structural topology design optimization for crashworthiness considering a prescribed and safe structural behavior through the dynamic equilibrium equation. This implementation, called here controlled crash behavior, or CCB, is very useful for design engineers in the automotive industry since it allows them to ‘prescribe’ a structural behavior of the vehicle at given locations of interest. The methodology is based on previous work from the author where the optimum topology is determined using a heuristic (optimality) criterion to attain a design with prescribed levels of plastic strains and stresses. The paper includes a simple beam example to demonstrate the CCB approach. Results are consistent with the formulation of the optimization problem.

scholarly journals Methods for Solving Generalized Nash Equilibrium

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Biao Qu ◽  
Jing Zhao
Keyword(s):  
Nash Equilibrium ◽  
Convergence Analysis ◽  
Equilibrium Problem ◽  
Unconstrained Optimization ◽  
Stationary Point ◽  
Optimization Problem ◽  
Generalized Nash Equilibrium Problem ◽  
Generalized Nash Equilibrium ◽  
Nash Equilibrium Problem ◽  
Globally Convergent

The generalized Nash equilibrium problem (GNEP) is an extension of the standard Nash equilibrium problem (NEP), in which each player's strategy set may depend on the rival player's strategies. In this paper, we present two descent type methods. The algorithms are based on a reformulation of the generalized Nash equilibrium using Nikaido-Isoda function as unconstrained optimization. We prove that our algorithms are globally convergent and the convergence analysis is not based on conditions guaranteeing that every stationary point of the optimization problem is a solution of the GNEP.

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