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Relative arbitrage: sharp time horizons and motion by curvature

Martin Larsson and Johannes Ruf

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We characterize the minimal time horizon over which any equity market with d ≥ 2 stocks and sufficient intrinsic volatility admits relative arbitrage. 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 R d that we call the minimum curvature flow.

Keywords: arbitrage; geometric flow; stochastic control; stochastic portfolio theory; Wiley deal (search for similar items in EconPapers)
JEL-codes: F3 G3 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2021-07-01
New Economics Papers: this item is included in nep-ore
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Published in Mathematical Finance, 1, July, 2021, 31(3), pp. 885 - 906. ISSN: 0960-1627

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