We derive abstract as well as deterministic conditions for the absence and existence of free lunch with vanishing risk, arbitrage, generalized arbitrage, and unbounded profit with bounded risk in a general multidimensional diffusion framework. Moreover, we give conditions for the absence and presence of financial bubbles. In particular, we provide criteria for the (strict local) martingale property of certain stochastic exponentials. As an application, we illustrate the influence of the market dimension, i.e. the number of stocks in the market, on free lunch with vanishing risk and generalized arbitrage. Our proofs are based on explosion criteria for martingale problems, local measure changes, and comparison arguments.
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