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

Moawia Alghalith

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.

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

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.

Paper Structure

This paper contains 6 sections, 46 equations.

Table of Contents

  1. Introduction
  2. Relaxing the differentiability assumption in Taylor theorem
  3. The portfolio model
  4. Extensions
  5. The portfolio and consumption
  6. The portfolio with a (stochastic) economic factor