Farinelli and Tibiletti (F-T) ratio, a general risk-reward performance measurement ratio, is popular due to its simplicity and yet generality that both Omega ratio and upside potential ratio are its special cases. The F-T ratios are ratios of average gains to average losses with respect to a...

We augment Tversky and Khaneman (1992) (“TK92”) Cumulative Prospect Theory (“CPT”) function space with a sample space for “states of nature”, and depict a commutative map of behavior on the augmented space. In particular, we use a homotopy lifting property to mimic behavioral...

We augment Tversky and Khaneman (1992) (“TK92”) Cumulative Prospect Theory (“CPT”) function space with a sample space for “states of nature”, and depict a commutative map of behavior on the augmented space. In particular, we use a homotopy lifting property to mimic behavioral...

We augment Tversky and Khaneman (1992) (TK92) Cumulative Prospect Theory (CPT) function space with a sample space for states of nature, and depict a commutative map of behavior on the augmented space. In particular, we use a homotopy lifting property to mimic behavioral stochastic processes...

The class of defensive online portfolio selection algorithms,designed for fi nite investment horizon, is introduced. The Game Constantly Rebalanced Portfolio and the Worst Case Game Constantly Rebalanced Portfolio, are presented and theoretically analyzed. The analysis exploits the rich set of...

The proof of the theorem of existence of the ruptures, namely the proof of maximality, is improved. The theorem may be used in economics and explain the well-known problems such as Allais’ paradox. Illustrated examples of ruptures are presented.

An introduction to interval analysis of distributions, as a new direction of interval analysis, is presented, including illustrated examples. New formulas and additional restrictions for intervals of moments, including mean value, are obtained. Among them are Novoselov formulas for moments and...

This paper studies the impact of background risk on the indifference curve. We first study the shape of the indifference curves for the investment with background risk for risk averters, risk seekers, and risk-neutral investors. Thereafter, we study the comparative statics of the change in the...

What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former – a so-called “belief-binarization rule” – without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from...

The goal of the present article is to define transformations (named here as auto-transformations) of probability density functions of random variables into similar functions having smaller sizes of their domains. In particular, auto-transformations from infinite to finite sizes of domains will...