New exact Taylor's expansions and simple solutions to PDEs

TL;DR

This paper introduces new exact Taylor's series with fixed coefficients, enabling the derivation of simple solutions to nonlinear PDEs and applications to portfolio models.

Contribution

It presents novel Taylor's expansions without remainders, facilitating straightforward solutions to complex PDEs and financial models.

Findings

New Taylor's series with fixed coefficients and no remainder

Simple solutions to nonlinear PDEs demonstrated

Application to portfolio modeling shown

Abstract

We provide new exact Taylor's series with fixed coefficients and without the remainder. We demonstrate the usefulness of this contribution by using it to obtain very simple solutions to (non-linear) PDEs. We also apply the method to the portfolio model.