Integration with respect to model-free price paths with jumps

TL;DR

This paper develops a method to define integrals of adapted strategies with respect to model-free price paths that have jumps, by approximating through simple integrals under mild growth conditions.

Contribution

It introduces a new approach to define integrals with respect to jump processes in a model-free setting, extending classical stochastic integration.

Findings

Defines integral as a limit of simple integrals for jump processes

Applicable to typical cadlag price paths with mild jump growth conditions

Provides a framework for model-free integration with jumps

Abstract

For every adapted, c\`agl\`ad process (strategy) $G$ and typical c\`adl\`ag price paths whose jumps satisfy some mild growth condition we define integral $G\cdot S$ as a limit of simple integrals.