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Relative arbitrage: Sharp time horizons and motion by curvature
Author(s) -
Larsson Martin,
Ruf Johannes
Publication year - 2021
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12303
Subject(s) - arbitrage , horizon , curvature , economics , portfolio , mathematics , mathematical economics , financial economics , geometry
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 and3 / ( 2 π )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 R d that we call the minimum curvature flow.