# Local Well-Posedness for Generalized Semilinear Black-Scholes Equations

## TL;DR

This paper establishes local well-posedness results for a class of nonlinear parabolic equations generalizing the Black-Scholes model, with initial data in L^p spaces, advancing the mathematical understanding of these models.

## Contribution

It proves local well-posedness for generalized nonlinear Black-Scholes equations with initial data in L^p spaces, a novel extension in mathematical finance modeling.

## Key findings

- Proved local well-posedness for the equations
- Extended analysis to initial data in L^p spaces
- Provided a mathematical foundation for nonlinear Black-Scholes models

## Abstract

We consider some parabolic equations which are model problems for a variety of nonlinear generalizations to the Black-Scholes equation of mathematical finance. In particular, we prove local well-posedness for the Cauchy problem with initial data in $L^{p}$ spaces.