This paper defines the concept of simple strategy and introduces three kinds of simple strategies: wealth-invariant, scale-invariant and "wealthier-accept more". For three commonly used utility function families: CARA, CRRA and DARA equivalent characterizations are obtained in terms of the...

This paper develops new methodological insights on Random Regret Minimization (RRM) models. It starts by showing that the classical RRM model is not scale-invariant, and that – as a result – the degree of regret minimization behavior imposed by the classical RRM model depends crucially on...

Recent research has established log-periodic power law (LPPL) patterns prior to the detonation of the German stock index (DAX) bubble in 1998. The purpose of this article is to explore whether a Langevin equation extracted from real world data can generate synthetic time series with comparable...

We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of the Fisher information measure. In such a way a clear analogy between these systems’ thermal properties and those of gases and fluids is seen to emerge in a natural fashion. We...

Random populations represented by stochastically scattered collections of real-valued points are abundant across many fields of science. Fractality, in the context of random populations, is conventionally associated with a Paretian distribution of the population's values.

In the homogeneous case of one-dimensional objects, we show that any relation that is positive and homothetic can be represented by a ratio-scale and a unique and constant biasing factor. This factor may favor or disfavor the preference for an object over another. In the first case, preferences...

Properties of low-variability periods in the time series are analysed. The theoretical approach is used to show the relationship between the multi-scaling of low-variability periods and multi-affinity of the time series. It is shown that this technically simple method is capable of revealing...

This article is the second one in a series on the use of scaling invariance in finance. In the first paper, we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects only, and which completely avoids the use of martingale techniques. In this...