Regularity of solutions to the parabolic fractional obstacle problem

TL;DR

This paper investigates the regularity of solutions to a parabolic fractional obstacle problem, motivated by financial models involving discontinuous stock price paths, and establishes near-optimal regularity results.

Contribution

It introduces a parabolic fractional obstacle problem and proves almost optimal regularity for its solutions, advancing the mathematical understanding of such models.

Findings

Established almost optimal regularity for solutions

Connected the problem to financial models with discontinuous paths

Extended regularity theory to a new class of parabolic fractional problems

Abstract

In this paper we study a parabolic version of the fractional obstacle problem, proving almost optimal regularity for the solution. This problem is motivated by an American option model proposed by Menton which introduces, into the theory of option evaluation, discontinuous paths in the dynamics of the stock's prices.