JEL classification: G14, G15, G20;
Keywords: Arbitrage, Bang-Bang rule, Non-cooperative game, Nash equilibrium, Optimal stopping, Optimal control, SA, Threshold strategies;
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.