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Relative arbitrage: Sharp time horizons and motion by curvature
Mathematical Finance ( IF 1.6 ) Pub Date : 2021-03-31 , DOI: 10.1111/mafi.12303
Martin Larsson 1 , Johannes Ruf 2
Affiliation  

We characterize the minimal time horizon over which any equity market with urn:x-wiley:09601627:media:mafi12303:mafi12303-math-0001 stocks and sufficient intrinsic volatility admits relative arbitrage with respect to the market portfolio. If urn:x-wiley:09601627:media:mafi12303:mafi12303-math-0002, the minimal time horizon can be computed explicitly, its value being zero if urn:x-wiley:09601627:media:mafi12303:mafi12303-math-0003 and urn:x-wiley:09601627:media:mafi12303:mafi12303-math-0004 if urn:x-wiley:09601627:media:mafi12303:mafi12303-math-0005. If urn:x-wiley:09601627:media:mafi12303:mafi12303-math-0006, the minimal time horizon can be characterized via the arrival time function of a geometric flow of the unit simplex in urn:x-wiley:09601627:media:mafi12303:mafi12303-math-0007 that we call the minimum curvature flow.

中文翻译:

相对套利:尖锐的时间范围和曲率运动

我们描述了任何拥有骨灰盒:x-wiley:09601627:媒体:mafi12303:mafi12303-math-0001股票和足够内在波动性的股票市场允许相对于市场投资组合进行相对套利的最小时间范围。如果骨灰盒:x-wiley:09601627:媒体:mafi12303:mafi12303-math-0002,可以显式计算最小时间范围,如果骨灰盒:x-wiley:09601627:媒体:mafi12303:mafi12303-math-0003并且骨灰盒:x-wiley:09601627:媒体:mafi12303:mafi12303-math-0004如果其值为零骨灰盒:x-wiley:09601627:媒体:mafi12303:mafi12303-math-0005。如果骨灰盒:x-wiley:09601627:媒体:mafi12303:mafi12303-math-0006,最小时间范围可以通过单位单纯形几何流的到达时间函数来表征骨灰盒:x-wiley:09601627:媒体:mafi12303:mafi12303-math-0007,我们称之为最小曲率流。
更新日期:2021-03-31
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