Existence & Regularity of Weak Solutions of Degenerate Parabolic PDE Models for the Pricing of Security Derivatives

TL;DR

This paper investigates the existence and regularity of weak solutions to degenerate parabolic PDEs used in pricing Asian options, employing finite difference schemes to establish solvability and analyze solution properties.

Contribution

It provides new results on the solvability and regularity of degenerate PDE models in financial mathematics, specifically for Asian option pricing.

Findings

Proved generalized solvability for degenerate boundary models

Analyzed regularity properties of solutions

Utilized finite difference schemes for solution construction

Abstract

This work is focused on the solvability of initial-boundary value problems for degenerate parabolic partial differential equations that arise in the pricing of Asian options, and on the investigation of differential and certain qualitative properties of solutions of such equations. The generalized solvability for such models with degeneracy at the boundaries is proven by employing solutions obtained from finite difference numerical schemes. Furthermore, the regularity of such solutions is studied.