Stochastic Dominance Efficiency Tests under Diversification

This paper focuses on Stochastic Dominance (SD) efficiency in a finite empirical panel data. We analytically characterize the sets of unsorted time series that dominate a given evaluated distribution by the First, Second, and Third order SD. Using these insights, we develop simple Linear Programming and 0-1 Mixed Integer Linear Programming tests of SD efficiency. The advantage to the earlier efficiency tests is that the proposed approach explicitly accounts for diversification. Allowing for diversification can both improve the power of the empirical SD tests, and enable SD based portfolio optimization. A simple numerical example illustrates the SD efficiency tests. Discussion on the application potential and the future research directions concludes.Stochastic Dominance, Protfolio Choice, Efficiency, Diversification, Mathematical Programming

On Classification-Calibration of Gamma-Phi Losses

Gamma-Phi losses constitute a family of multiclass classification loss functions that generalize the logistic and other common losses, and have found application in the boosting literature. We establish the first general sufficient condition for the classification-calibration of such losses. In addition, we show that a previously proposed sufficient condition is in fact not sufficient.Comment: 21 page

Currencies in resource theories

How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like perfectly independent copies of states or exact knowledge of a quantum state. Here we introduce the general tool of currencies to quantify realistic descriptions of resources, applicable in experimental settings when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when there is no obvious way to decompose a global space into subsystems. Currencies are a special set of resources chosen to quantify all others - like Bell pairs in LOCC or a lifted weight in thermodynamics. We show that from very weak assumptions on the theory we can already find useful currencies that give us necessary and sufficient conditions for resource conversion, and we build up more results as we impose further structure. This work is an application of Resource theories of knowledge [arXiv:1511.08818], generalizing axiomatic approaches to thermodynamic entropy, work and currencies made of local copies.Comment: 13 pages + appendix. Contains a one-page summary of the paper Resource theories of knowledge [arXiv:1511.08818