We derive integral tests for the existence and absence of arbitrage in a financial market with one risky asset which is either modeled as stochastic exponential of an Itô process or a positive diffusion with Markov switching. In particular, we derive conditions for the existence of the minimal martingale measure. We also show that for Markov switching models the minimal martingale measure preserves the independence of the noise and we study how the minimal martingale measure can be modified to change the structure of the switching mechanism. Our main mathematical tools are new criteria for the martingale and strict local martingale property of certain stochastic exponentials.

中文翻译：

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连续金融市场无套利

我们得出一种具有风险资产的金融市场中套利的存在和不存在的整体检验，该资产被建模为Itô过程的随机指数或马尔可夫切换的正扩散。特别是，我们得出了最小mar测度的存在条件。我们还表明，对于马尔可夫切换模型，最小mar度量保留了噪声的独立性，并且我们研究了如何修改最小mar度量以改变切换机制的结构。我们的主要数学工具是the的新准则和某些随机指数的严格本地mar性质。