ISSN:
 2164-6066

eISSN:
 2164-6074

All Issues

Volume 5, 2018

Volume 4, 2017

Volume 3, 2016

Volume 2, 2015

Volume 1, 2014

The Journal of Dynamics and Games (JDG) is an applied mathematicsjournal that publishes high quality peer-review and expository papersin all research areas of expertise of its editors. The main focus ofJDG is in the interface of Dynamical Systems and Game Theory. Click here for more information

SUBMISSIONS TO REGULAR ISSUES
The submissions to JDG regular issues are done by email to the editors in chief or directly to one of the editors. The authors should ask for an email from the editors in chief confirming the reception of the paper.

JDG Flyer

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 4 issues a year in January, April, July and October.
  • Publishes online only.
  • Indexed in Emerging Sources Citation Index, MathSciNet and Zentralblatt MATH.
  • Archived in Portico and CLOCKSS.
  • JDG is a publication of the American Institute of Mathematical Sciences. All rights reserved.

Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.

Select all articles

Export/Reference:

Robust portfolio decisions for financial institutions
Ioannis Baltas, Anastasios Xepapadeas and Athanasios N. Yannacopoulos
2018, 5(2) : 61-94 doi: 10.3934/jdg.2018006 +[Abstract](475) +[HTML](389) +[PDF](721.98KB)
Abstract:

The present paper aims to study a robust-entropic optimal control problem arising in the management of financial institutions. More precisely, we consider an economic agent who manages the portfolio of a financial firm. The manager has the possibility to invest part of the firm's wealth in a classical Black-Scholes type financial market, and also, as the firm is exposed to a stochastic cash flow of liabilities, to proportionally transfer part of its liabilities to a third party as a means of reducing risk. However, model uncertainty aspects are introduced as the manager does not fully trust the model she faces, hence she decides to make her decision robust. By employing robust control and dynamic programming techniques, we provide closed form solutions for the cases of the (ⅰ) logarithmic; (ⅱ) exponential and (ⅲ) power utility functions. Moreover, we provide a detailed study of the limiting behavior, of the associated stochastic differential game at hand, which, in a special case, leads to break down of the solution of the resulting Hamilton-Jacobi-Bellman-Isaacs equation. Finally, we present a detailed numerical study that elucidates the effect of robustness on the optimal decisions of both players.

Games with nested constraints given by a level structure
Francisco Sánchez-Sánchez and Miguel Vargas-Valencia
2018, 5(2) : 95-107 doi: 10.3934/jdg.2018007 +[Abstract](510) +[HTML](255) +[PDF](386.75KB)
Abstract:

In this paper we propose new games that satisfy nested constraints given by a level structure of cooperation. This structure is defined by a family of partitions on the set of players. It is ordered in such a way that each partition is a refinement of the next one. We propose a value for these games by adapting the Shapley value. The value is characterized axiomatically. For this purpose, we introduce a new property called class balance contributions by generalizing other properties in the literature. Finally, we introduce a multilinear extension of our games and use it to obtain an expression for calculating the adapted Shapley value.

Constrained stochastic differential games with additive structure: Average and discount payoffs
Beatris Adriana Escobedo-Trujillo, Alejandro Alaffita-Hernández and Raquiel López-Martínez
2018, 5(2) : 109-141 doi: 10.3934/jdg.2018008 +[Abstract](419) +[HTML](267) +[PDF](599.26KB)
Abstract:

This paper deals with two-person nonzero-sum stochastic differential games (SDGs) with an additive structure, subject to constraints that are additive also. Our main objective is to give conditions for the existence of constrained Nash equilibria for the case of infinite-horizon discounted payoff. This is done by means of the Lagrange multipliers approach combined with dynamic programming arguments. Then, following the vanishing discount approach, the results in the discounted case are used to obtain constrained Nash equilibria in the case of long-run average payoff.

A risk minimization problem for finite horizon semi-Markov decision processes with loss rates
Qiuli Liu and Xiaolong Zou
2018, 5(2) : 143-163 doi: 10.3934/jdg.2018009 +[Abstract](319) +[HTML](303) +[PDF](559.55KB)
Abstract:

This paper deals with the risk probability for finite horizon semi-Markov decision processes with loss rates. The criterion to be minimized is the risk probability that the total loss incurred during a finite horizon exceed a loss level. For such an optimality problem, we first establish the optimality equation, and prove that the optimal value function is a unique solution to the optimality equation. We then show the existence of an optimal policy, and develop a value iteration algorithm for computing the value function and optimal policies. We also derive the approximation of the value function and the rules of iteration. Finally, a numerical example is given to illustrate our results.

Stable manifold market sequences
E. Camouzis, H. Kollias and I. Leventides
2018, 5(2) : 165-185 doi: 10.3934/jdg.2018010 +[Abstract](247) +[HTML](183) +[PDF](535.26KB)
Abstract:

In this article, we construct examples of discrete-time, dynamic, partial equilibrium, single product, competition market sequences, namely, \begin{document}$\{m_{t}\}_{t = 0}^{∞}$\end{document}, in which, potentially active firms, are countably infinite, the inverse demand function is linear, and the initial market \begin{document}$m_0$\end{document} is null. For Cournot markets, in which, the number of firms is defined exogenously, as a finite positive integer, namely \begin{document}$n: n>3$\end{document}, the long term behavior of the quantity supplied, into the market, by Cournot firms is not well explored and is unknown. In this article, we conjecture, that in all such cases, the Cournot equilibrium, provided that it exists, is unreachable. We construct Cournot market sequences, which might be viewed, as appropriate resource tools, through which, the "unreachability" of Cournot equilibrium points is being resolved. Our construction guidelines are, the stable manifolds of Cournot equilibrium points. Moreover, if the number of active firms, increases to infinity and the marginal costs of all active firms are identical, the aggregate market supply, increases to a competitive limit and each firm, at infinity, faces a market price equal to its marginal cost. Hence, the market sequence approaches a perfectly competitive equilibrium. In the case, where marginal costs are not identical, we show, that there exists a market sequence, \begin{document}$\{m_{t}\}_{t = 0}^{∞}$\end{document}, which approaches an infinite dimensional Cournot equilibrium point. In addition, we construct a sequence of Cournot market sequences, namely, \begin{document}$\{m_{it}\}_{t = 0}^{∞}, i ≥ 1$\end{document}, which, for each, \begin{document}$i$\end{document}, approaches an imperfectly competitive equilibrium. The sequence of the equilibrium points and the double sequence, \begin{document}$\{m_{it}\}$\end{document}, both approach, the equilibrium, at infinity, of the market sequence, \begin{document}$\{m_t\}$\end{document}.

Corrigendum to "A Malthus-Swan-Solow model of economic growth"
Luis C. Corchón
2018, 5(2) : 187-187 doi: 10.3934/jdg.2018011 +[Abstract](208) +[HTML](150) +[PDF](133.0KB)
Abstract:
General limit value in dynamic programming
Jérôme Renault
2014, 1(3) : 471-484 doi: 10.3934/jdg.2014.1.471 +[Abstract](478) +[PDF](385.9KB) Cited By(8)
Pure and Random strategies in differential game with incomplete informations
Pierre Cardaliaguet, Chloé Jimenez and Marc Quincampoix
2014, 1(3) : 363-375 doi: 10.3934/jdg.2014.1.363 +[Abstract](533) +[PDF](386.0KB) Cited By(6)
Existence of the uniform value in zero-sum repeated games with a more informed controller
Fabien Gensbittel, Miquel Oliu-Barton and Xavier Venel
2014, 1(3) : 411-445 doi: 10.3934/jdg.2014.1.411 +[Abstract](429) +[PDF](550.1KB) Cited By(6)
Discrete time dynamic oligopolies with adjustment constraints
Chrystie Burr, Laura Gardini and Ferenc Szidarovszky
2015, 2(1) : 65-87 doi: 10.3934/jdg.2015.2.65 +[Abstract](434) +[PDF](535.9KB) Cited By(4)
Reversibility and oscillations in zero-sum discounted stochastic games
Sylvain Sorin and Guillaume Vigeral
2015, 2(1) : 103-115 doi: 10.3934/jdg.2015.2.103 +[Abstract](406) +[PDF](364.9KB) Cited By(4)
Approachability, regret and calibration: Implications and equivalences
Vianney Perchet
2014, 1(2) : 181-254 doi: 10.3934/jdg.2014.1.181 +[Abstract](518) +[PDF](897.5KB) Cited By(4)
Nonzero-sum stochastic differential games with additive structure and average payoffs
Beatris Adriana Escobedo-Trujillo and José Daniel López-Barrientos
2014, 1(4) : 555-578 doi: 10.3934/jdg.2014.1.555 +[Abstract](577) +[PDF](527.0KB) Cited By(4)
Paths to stability in the assignment problem
Bettina Klaus and Frédéric Payot
2015, 2(3&4) : 257-287 doi: 10.3934/jdg.2015004 +[Abstract](514) +[PDF](538.5KB) Cited By(3)
Optimal strategies for operating energy storage in an arbitrage or smoothing market
Lisa C Flatley, Robert S MacKay and Michael Waterson
2016, 3(4) : 371-398 doi: 10.3934/jdg.2016020 +[Abstract](599) +[PDF](831.3KB) Cited By(3)
Dynamics of human decisions
Renato Soeiro, Abdelrahim Mousa, Tânia R. Oliveira and Alberto A. Pinto
2014, 1(1) : 121-151 doi: 10.3934/jdg.2014.1.121 +[Abstract](519) +[PDF](2417.1KB) Cited By(3)
Robust portfolio decisions for financial institutions
Ioannis Baltas, Anastasios Xepapadeas and Athanasios N. Yannacopoulos
2018, 5(2) : 61-94 doi: 10.3934/jdg.2018006 +[Abstract](475) +[HTML](389) +[PDF](721.98KB) PDF Downloads(64)
Hyperopic topologies on $l^{∞}$
Paulo Klinger Monteiro, Jaime Orrillo and Rudy José Rosas Bazán
2018, 5(1) : 1-7 doi: 10.3934/jdg.2018001 +[Abstract](710) +[HTML](316) +[PDF](346.6KB) PDF Downloads(55)
On the linearity property for allocation problems and bankruptcy problems
Joss Sánchez-Pérez
2018, 5(1) : 9-20 doi: 10.3934/jdg.2018002 +[Abstract](440) +[HTML](285) +[PDF](333.3KB) PDF Downloads(38)
Constrained stochastic differential games with additive structure: Average and discount payoffs
Beatris Adriana Escobedo-Trujillo, Alejandro Alaffita-Hernández and Raquiel López-Martínez
2018, 5(2) : 109-141 doi: 10.3934/jdg.2018008 +[Abstract](419) +[HTML](267) +[PDF](599.26KB) PDF Downloads(33)
Equivalences between two matching models: Stability
Paola B. Manasero
2017, 4(5) : 1-19 doi: 10.3934/jdg.2018013 +[Abstract](151) +[HTML](163) +[PDF](431.57KB) PDF Downloads(31)
Transitional dynamics, externalities, optimal subsidy, and growth
Enrique R. Casares, Lucia A. Ruiz-Galindo and María Guadalupe García-Salazar
2018, 5(1) : 41-59 doi: 10.3934/jdg.2018005 +[Abstract](411) +[HTML](412) +[PDF](485.2KB) PDF Downloads(29)
Games with nested constraints given by a level structure
Francisco Sánchez-Sánchez and Miguel Vargas-Valencia
2018, 5(2) : 95-107 doi: 10.3934/jdg.2018007 +[Abstract](510) +[HTML](255) +[PDF](386.75KB) PDF Downloads(29)
Pricing bond options in emerging markets: A case study
Guillermo Magnou, Ernesto Mordecki and Andrés Sosa
2018, 5(1) : 21-30 doi: 10.3934/jdg.2018003 +[Abstract](507) +[HTML](264) +[PDF](329.0KB) PDF Downloads(27)
A solution for discrete cost sharing problems with non rival consumption
Adriana Navarro-Ramos and William Olvera-Lopez
2018, 5(1) : 31-39 doi: 10.3934/jdg.2018004 +[Abstract](439) +[HTML](242) +[PDF](295.3KB) PDF Downloads(26)
Critical transitions and Early Warning Signals in repeated Cooperation Games
Christian Hofer, Georg Jäger and Manfred Füllsack
2017, 4(5) : 1-8 doi: 10.3934/jdg.2018014 +[Abstract](178) +[HTML](129) +[PDF](359.38KB) PDF Downloads(24)

Editors

Referees

Librarians

Email Alert

[Back to Top]