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Stochastic Finance, 4th Edition by Alexander Schied, Hans Föllmer

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5Dynamic arbitrage theory

In this chapter we develop a dynamic version of the arbitrage theory of Chapter 1. Here we will work in a multiperiod setting, where the stochastic price fluctuation of a financial asset is described as a stochastic process in discrete time. Portfolios will be successively readjusted, taking into account the information available at each time. Such a dynamic trading strategy may produce a positive expected gain. If it does so without any downside risk then it is called an arbitrage opportunity. In its weakest form, market efficiency requires that such arbitrage opportunities are excluded.

In Section 5.2 we show that an arbitrage-free model is characterized by the existence of an equivalent martingale measure. Under such ...

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