<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Exchange rate and its related risk management are too important for main participants in foreign exchange markets. There are many approaches developed in the literature for studying risk management say arbitrage detection, say finding replication portfolio. However, in the current paper, arbitrage opportunities are studied using the game theory perspective. This paper proposes different types of games played in a specified foreign exchange market in the presence of three exchange rates. Proposed games are exchange rate games in two cases of no arbitrage and existence of arbitrage, optimal stopping game, the arbitrage game, threshold strategies used in global game and Non-cooperative exchange rate game. Most of cases, the bang-bang rule of optimal control is used for finding the Nash equilibriums (NE). However, simulated and stochastic approximation (SA) solutions are also given. Most highlights of the current paper are: (I) considering two types of arbitrage opportunities, simultaneously, (II) translating arbitrage detection as game theory concepts, (III) solving the problem using techniques of optimal control theory. Finally concluding remarks are proposed.</p>
</abstract>

Exchange rate and its related risk management are too important for main participants in foreign exchange markets. There are many approaches developed in the literature for studying risk management say arbitrage detection, say finding replication portfolio. However, in the current paper, arbitrage opportunities are studied using the game theory perspective. This paper proposes different types of games played in a specified foreign exchange market in the presence of three exchange rates. Proposed games are exchange rate games in two cases of no arbitrage and existence of arbitrage, optimal stopping game, the arbitrage game, threshold strategies used in global game and Non-cooperative exchange rate game. Most of cases, the bang-bang rule of optimal control is used for finding the Nash equilibriums (NE). However, simulated and stochastic approximation (SA) solutions are also given. Most highlights of the current paper are: (I) considering two types of arbitrage opportunities, simultaneously, (II) translating arbitrage detection as game theory concepts, (III) solving the problem using techniques of optimal control theory. Finally concluding remarks are proposed.

Games in a foreign exchange market and solutions

Financial Internet Quarterly

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Games in a foreign exchange market and solutions"}

Exchange rate and its related risk management are too important for main participants in foreign exchange markets. There are many approaches developed in the...

Games in a foreign exchange market and solutions

Published Online: Oct 06, 2023

Page range: 75 - 86

Received: Jun 15, 2023

Accepted: Aug 25, 2023

DOI: https://doi.org/10.2478/fiqf-2023-0020

Keywords
Arbitrage, Bang-Bang rule, Non-cooperative game, Nash equilibrium, Optimal stopping, Optimal control, SA, Threshold strategies

© 2023 Reza Habibi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Games in a foreign exchange market and solutions

Published Online: Oct 06, 2023

Page range: 75 - 86

Received: Jun 15, 2023

Accepted: Aug 25, 2023

DOI: https://doi.org/10.2478/fiqf-2023-0020

KeywordsArbitrage, Bang-Bang rule, Non-cooperative game, Nash equilibrium, Optimal stopping, Optimal control, SA, Threshold strategies

© 2023 Reza Habibi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Arbitrage, Bang-Bang rule, Non-cooperative game, Nash equilibrium, Optimal stopping, Optimal control, SA, Threshold strategies