Nonparametric methods for the estimation of the Levy density of a Levy process X are developed. Estimators that can be writtenin terms of the "jumps" of X are introduced, and so are discrete-data based approximations. A model selection approach made up oftwo steps is investigated. The first step...

We consider an evolving ensemble assembled from a set of n different elements via a stochastic growth process in which independent and identically distributed copies of the elements arrive randomly in time, and their statistics are governed by Zipf’s law. The associated “Heaps process” is...

This article extends the exchange option model of Margrabe, where the distributions of both stock prices are log-normal with correlated Wiener components, to allow the underlying assets to be driven by jump-diffusion processes of the type originally introduced by Merton. We introduce the...

This paper presents a profound connection between Gini’s index and extreme-value statistics. Gini’s index is a quantitative gauge for the evenness of probability laws defined on the positive half-line, and is the common measure of societal egalitarianism applied in Economics and in the...

Consider a finite sequence of independent–though not, necessarily, identically distributed–real-valued random scores. If the scores are absolutely continuous random variables, the sequence possesses a unique maximum (minimum). We say that “maximal (minimal) independence” holds if the...

This paper contains an analytical formulation for performance measurement of an unreliable production-storage operation where production and demand rates for a single item are subject to random fluctuations in the operating environment. These fluctuations are represented as transitions among the...

The growth empirics of two separate but related issues are studied. In the first, the annual data on GDP per person (GDPpp) for Brazil, 1822-2000, and the US, 1869-1996, were converted into arrival times for innovations defined as permanent increments to GDPpp of given size (e.g. 3%). We say an...