On a degenerate parabolic equation arising in pricing of Asian options

TL;DR

This paper proves that a degenerate parabolic PDE related to Asian option pricing has a classical solution despite boundary degeneracy and non-smooth conditions, clarifying solution regularity.

Contribution

It establishes the regularity of solutions for a degenerate PDE in Asian option pricing, resolving previous uncertainties about solution smoothness.

Findings

The generalized solution is a classical solution.

Regularity is achieved despite boundary degeneracy.

Addresses non-smooth boundary conditions.

Abstract

We study a certain one dimensional, degenerate parabolic partial differential equation with a boundary condition which arises in pricing of Asian options. Due to degeneracy of the partial differential operator and the non-smooth boundary condition, regularity of the generalized solution of such a problem remained unclear. We prove that the generalized solution of the problem is indeed a classical solution.