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11 papers
Portfolio optimization in incomplete markets and price constraints determined by maximum entropy in the mean
Argimiro Arratia, Henryk Gzyl
A solution to a portfolio optimization problem is always conditioned by constraints on the initial capital and the price of the available market assets. If a risk neutral measure i…
Lorentz covariant physical Brownian motion: Classical and quantum
Henryk Gzyl
In this work, we re-examine the Goldstein-Kaç velocity switching model from two points of view. On the one hand, we prove that the forward and backward Chapman-Kolmogorov equations…
Joint probabilities under expected value constraints, transportation problems, maximum entropy in the mean, and geometry in the space of probabilities
Henryk Gzyl
There are interesting extensions of the problem of determining a joint probability with known marginals. On the one hand, one may impose size constraints on the joint probabilities…
From generalized arithmetic means to geodesics to Hamilton dynamics to Bregman divergences
Henryk Gzyl
Here we examine some connections between the notions of generalized arithmetic means, geodesics, Lagrange-Hamilton dynamics and Bregman divergences. In a previous paper we develope…
A predictive approach to generalized arithmetic means
Henryk Gzyl
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometr…
Geometry and clustering with metrics derived from separable Bregman divergences
Erika Gomes-Gonçalves, Henryk Gzyl, Frank Nielsen
Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its co…