Relative Arbitrage: Sharp Time Horizons and Motion by Curvature

2020/03/30 by Larsson, Martin, Ruf, Johannes · 2 citations
#35J60 #49L25 #60G44 #91G10 #Analysis of PDEs (math.AP) #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR)

paper · doi:10.48550/arxiv.2003.13601

Abstract

We characterize the minimal time horizon over which any equity market with d ≥ 2 stocks and sufficient intrinsic volatility admits relative arbitrage with respect to the market portfolio. If d ∈ \2,3\, the minimal time horizon can be computed explicitly, its value being zero if d=2 and √(3)/(2π) if d=3. If d ≥ 4, the minimal time horizon can be characterized via the arrival time function of a geometric flow of the unit simplex in \mathbb R^d that we call the minimum curvature flow.

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