Universal portfolios generated by the reverse f and Bregman divergences

2021 ◽  
Author(s):  
Tan Choon Peng ◽  
Kuang Kee Seng
Keyword(s):  
Bregman Divergences ◽  
Universal Portfolios

scholarly journals A Note on Universal Bilinear Portfolios

2021 ◽  
Vol 9 (1) ◽  
pp. 11
Author(s):  
Alex Garivaltis
Keyword(s):  
Growth Factor ◽  
Trading Strategy ◽  
Weighted Averaging ◽  
Asset Market ◽  
Best Constant ◽  
Capital Growth ◽  
Universal Portfolios ◽  
Universal Portfolio ◽  
Technical Sense ◽  
Constant Rebalanced Portfolios

This note provides a neat and enjoyable expansion and application of the magnificent Ordentlich-Cover theory of “universal portfolios”. I generalize Cover’s benchmark of the best constant-rebalanced portfolio (or 1-linear trading strategy) in hindsight by considering the best bilinear trading strategy determined in hindsight for the realized sequence of asset prices. A bilinear trading strategy is a mini two-period active strategy whose final capital growth factor is linear separately in each period’s gross return vector for the asset market. I apply Thomas Cover’s ingenious performance-weighted averaging technique to construct a universal bilinear portfolio that is guaranteed (uniformly for all possible market behavior) to compound its money at the same asymptotic rate as the best bilinear trading strategy in hindsight. Thus, the universal bilinear portfolio asymptotically dominates the original (1-linear) universal portfolio in the same technical sense that Cover’s universal portfolios asymptotically dominate all constant-rebalanced portfolios and all buy-and-hold strategies. In fact, like so many Russian dolls, one can get carried away and use these ideas to construct an endless hierarchy of ever more dominant H-linear universal portfolios.

On the uniform concentration bounds and large sample properties of clustering with Bregman divergences

Stat ◽  
2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Debolina Paul ◽  
Saptarshi Chakraborty ◽  
Swagatam Das
Keyword(s):  
Large Sample ◽  
Bregman Divergences ◽  
Concentration Bounds

A STUDY ON MALAYSIA STOCKS USING DISTRIBUTION BASED UNIVERSAL PORTFOLIOS

2021 ◽  
Vol 131 (1) ◽  
pp. 17-28
Author(s):  
Sook Theng Pang ◽  
How Hui Liew ◽  
Kah Hong Tan
Keyword(s):  
Universal Portfolios

scholarly journals On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 221 ◽  
Author(s):  
Frank Nielsen
Keyword(s):  
Iterative Algorithm ◽  
Bregman Divergences ◽  
Leibler Divergence ◽  
Probability Densities ◽  
Jensen Shannon Divergence

The Jensen–Shannon divergence is a renown bounded symmetrization of the Kullback–Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the scalar α -Jensen–Bregman divergences and derive thereof the vector-skew α -Jensen–Shannon divergences. We prove that the vector-skew α -Jensen–Shannon divergences are f-divergences and study the properties of these novel divergences. Finally, we report an iterative algorithm to numerically compute the Jensen–Shannon-type centroids for a set of probability densities belonging to a mixture family: This includes the case of the Jensen–Shannon centroid of a set of categorical distributions or normalized histograms.

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