Self-Financing Trading and the Ito-Doeblin Lemma

TL;DR

This paper clarifies the concept of self-financing trading strategies in quantitative finance, emphasizing its foundational role and the intersection with stochastic calculus, especially through the lens of the Ito-Doeblin lemma.

Contribution

It provides a clear explanation of self-financing strategies and highlights ongoing uncertainties, connecting stochastic calculus with financial modeling.

Findings

Clarifies the concept of self-financing trading strategies.

Highlights the intersection of stochastic calculus and finance.

Addresses uncertainties in the foundational understanding.

Abstract

The objective of the note is to remind readers on how self-financing works in Quantitative Finance. The authors have observed continuing uncertainty on this issue which may be because it lies exactly at the intersection of stochastic calculus and finance. The concept of a self-financing trading strategy was originally, and carefully, introduced in (Harrison and Kreps 1979) and expanded very generally in (Harrison and Pliska 1981).