无鞅测度的金融市场扩散模型
Diffusion-based models for financial markets without martingale measures
摘要：
我们考虑一类基于扩散的模型，并表明，即使在没有一个等价的本地鞅测度，金融市场可能仍然是可行的，在这个意义上，强形式的套利被排除在外，投资组合优化问题可以有意义地解决。部分依赖于最近的文献，我们提供了必要和充分条件的市场生存的风险过程和鞅平减指数的市场价格。无论存在的鞅测度，我们表明，金融市场可能仍然是完整的和或有债权可以在原来的（现实世界）的概率测度下，如果我们使用作为numeraire的增长最优投资组合。
英文摘要：
We consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and portfolio optimisation problems can be meaningfully solved. Relying partly on the recent literature, we provide necessary and sufficient conditions for market viability in terms of the market price of risk process and martingale deflators. Regardless of the existence of a martingale measure, we show that the financial market may still be complete and contingent claims can be valued under the original (real-world) probability measure, provided we use as numeraire the Growth-Optimal Portfolio.
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