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Arbitrage is making a certain profit in excess of the risk-free rate of return. Within the language of quantitative finance we can say that an arbitrage opportunity is a portfolio of zero value nowadays that is of positive value with positive probability in the future and of negative value with zero probability in the future.
The assumption that here are no arbitrage opportunities in the market is fundamental to typical finance theory. This idea is popularly termed as ‘there’s no that thing as a free lunch.’