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 .
We derive abstract as well as deterministic conditions for the absence and existence of arbitrage and financial bubbles in a general (multi- and infinite-dimensional) semimartingale-diffusion markets, and a Heath-Jarrow-Morton-Musiela framework. We also provide deterministic conditions for the martingale property of stochastic exponentials which are driven by solution to generalized martingale problems, respectively stochastic partial differential equations . As an application, we construct a financial market in which the number of assets determines the absence of arbitrage while the sources of risk have the same dimension .
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free lunch with vanishing risk, arbitrage , generalized arbitrage, and unbounded profit with bounded risk
arbitrage and financial bubbles
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multidimensional diffusion framework. Moreover, we give conditions for the absence and presence of financial bubbles. In particular, we provide criteria for the (strict local)
(multi- and infinite-dimensional) semimartingale-diffusion markets, and a Heath-Jarrow-Morton-Musiela framework. We also provide deterministic conditions for the
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certain stochastic exponentials
stochastic exponentials which are driven by solution to generalized martingale problems, respectively stochastic partial differential equations
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illustrate the influence of the market dimension, i.e.
construct a financial market in which
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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
assets determines the absence of arbitrage while the sources of risk have the same dimension