Relaxing the Differentiability Assumption in Taylor Theorem and Optimization: Applications to the HJB PDE and Finance

TL;DR

This paper introduces non-differentiable Taylor expansions, providing new solutions to PDEs and demonstrating applications in finance, thereby broadening the scope of Taylor's theorem and optimization techniques.

Contribution

It presents a novel approach to Taylor expansions that relax differentiability requirements, enabling new solutions to PDEs and applications in financial modeling.

Findings

New non-differentiable Taylor expansions developed

Provided novel solutions to partial differential equations

Applied methods successfully in financial contexts

Abstract

We introduce Taylor expansions that do not require the differentiability. We also provide new solutions to partial differential equations. We apply our methods to finance.