Partial regularity of viscosity solutions for a class of Kolmogorov equations arising from mathematical finance

TL;DR

This paper proves that certain viscosity solutions of Kolmogorov equations in mathematical finance are smoothly differentiable on specific subspaces, enhancing understanding of their regularity properties.

Contribution

It establishes partial $C^{1,eta}$ regularity of viscosity solutions for a class of Kolmogorov equations relevant to finance, using PDE techniques.

Findings

Viscosity solutions are $C^{1,eta}$ on finite-dimensional subspaces.

The results apply to equations arising in derivative pricing and hedging.

Provides new regularity insights for solutions in mathematical finance.

Abstract

We study value functions which are viscosity solutions of certain Kolmogorov equations. Using PDE techniques we prove that they are $C^{1,\alpha}$ regular on special finite dimensional subspaces. The problem has origins in pricing and hedging of derivatives of risky assets in mathematical finance.