Exponentially concave functions and high dimensional stochastic portfolio theory
Soumik Pal
Stochastic Processes and their Applications, 2019, vol. 129, issue 9, 3116-3128
Abstract:
We construct an explicit example of asymptotic short term relative arbitrage. Specifically, for every n we assume an n dimensional semimartingale market model that starts from a heavy-tailed initial position in the unit simplex and impose weak assumptions on its volatility. We then construct a sequence of portfolios, one for each dimension, that outperform the market portfolio in dimension n by an amount Mn by time δn with a probability at least 1−qn. Here Mn→∞ exponentially fast in n and δn,qn decrease to zero. Moreover, these portfolios never underperform below a pre-specified lower bound. The key fact is that it is possible to construct a sequence of exponentially concave functions on the unit simplex of increasing concavity because the typical diameter of the unit simplex in dimension n is O(1∕n).
Keywords: Stochastic portfolio theory; Relative arbitrage; Short term arbitrage; Exponentially concave functions; High-dimensional finance (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:9:p:3116-3128
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DOI: 10.1016/j.spa.2018.09.004
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