# Interior second derivative estimates for nonlinear diffusions

## TL;DR

This paper extends estimates for fully nonlinear parabolic equations, including singular and degenerate cases, with applications to option pricing models involving market impact.

## Contribution

It generalizes existing estimates to broader classes of nonlinear parabolic equations, including non-homogeneous, singular, and degenerate cases.

## Key findings

- Derived new second derivative estimates for nonlinear diffusions.
- Applied estimates to models in option pricing with market impact.
- Extended classical results to non-homogeneous and degenerate equations.

## Abstract

By an extension of of some estimates due to Crandall and Pierre and Di Benedetto we derive consequences for fully nonlinear parabolic equations of the form $\dt v + F(t,x,D^2v)=0$, where $F$ can be both singular and degenerate elliptic and also non-homogeneous. Such equations appear in the theory of option pricing with market impact.