English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the following problem in stochastic portfolio theory. Are thereportfolios that are relative arbitrages with respect to the market portfolioover very short periods of time under realistic assumptions? We answer aslightly relaxed question affirmative in the following high dimensional sense,where dimension refers to the number of stocks being traded. Very roughly,suppose that for every dimension we have a continuous semimartingale marketsuch that (i) the vector of market weights in decreasing order has a stationaryregularly varying tail with an index between $-1$ and $-1/2$ and (ii) zero isnot a limit point of the relative volatilities of the stocks. Then, given aprobability $\eta < 1$ arbitrarily close to one, two arbitrarily small$\epsilon, \delta >0$, and an arbitrarily high positive amount $M$, for allhigh enough dimensions, it is possible to construct a functionally generatedportfolio such that, with probability at least $\eta$, its relative value withrespect to the market at time $\delta$ is at least $M$, and never goes below$(1-\epsilon)$ during $[0, \delta]$. There are two phase transitions; if theindex of the tail is less than $-1$ or larger than $-1/2$. The constructionuses properties of regular variation, high-dimensional convex geometry andconcentration of measure under Dirichlet distributions. We crucially use thenotion of $(K,N)$ convex functions introduced by Erbar, Kuwada, Sturm in thecontext of curvature-dimension conditions and Bochner's inequalities.

Exponentially concave functions and high dimensional stochastic portfolio theory