On the Extreme Flights of One-Sided Levy Processes

TL;DR

This paper analyzes the statistical properties of extreme flights in One-sided Levy Processes, focusing on hierarchy and contribution of extreme flights, with explicit results for selfsimilar and power-law tail classes.

Contribution

It provides new insights into the hierarchy and relative contributions of extreme flights in OLPs, extending results to broader classes with power-law tails.

Findings

Hierarchical relationships among extreme flights are explicitly characterized.

Relative contributions of extreme flights to the total process are quantified.

Results are extendable to OLPs with arbitrary power-law flight tails.

Abstract

We explore the statistical behavior of the order statistics of the flights of One-sided Levy Processes (OLPs). We begin with the study of the extreme flights of general OLPs,and then focus on the class of selfsimilar processes,investigating the following issues:(i)the inner hierarchy of the extreme flights - for example:how big is the 7th largest flight relative to the 2nd largest one?; and,(ii)the relative contribution of the extreme flights to the entire 'flight aggregate' - for example: how big is the 3rd largest flight relative to the OLP's value?. Furthermore, we show that all 'hierarchical' results obtained - but not the 'aggregate' results - are explicitly extendable to the class of OLPs with arbitrary power-law flight tails (which is far larger than the selfsimilar class).