On the Yor integral and a system of polynomials related to the Kontorovich-Lebedev transform

TL;DR

This paper explores the Yor integral's representations, its connection to the Kontorovich-Lebedev transform, and introduces new properties of related polynomials, enhancing tools for financial mathematics applications.

Contribution

It establishes novel representations of the Yor integral and analyzes a related polynomial system, providing new properties and explicit formulas.

Findings

Yor integral related to Kontorovich-Lebedev transform

Derived asymptotic behavior of polynomials for large degrees

Provided explicit formulas for polynomial coefficients

Abstract

In this paper we establish different representations of the so-called Yor integral, which is one of the key ingredient in mathematical finance, in particular, to compute normalized prices of Asian options. We show, that the Yor integral is related with the Kontorovich-Lebedev transform. Also we discuss its relationship with a system of polynomials recently introduced by the author. We derive new important properties of these polynomials, including upper bounds, an exact asymptotic behavior for large values of their degree and explicit formula of coefficients.