Self-dual continuous processes

TL;DR

This paper explores the structure and properties of quasi self-dual continuous semimartingales, linking their symmetry features to financial hedging strategies and characterizing Ocone martingales through self-duality.

Contribution

It provides a structural characterization of quasi self-dual processes and a new way to identify Ocone martingales using strong self-duality conditions.

Findings

Structural results for continuous quasi self-dual processes

Characterization of continuous Ocone martingales via self-duality

Insights into symmetry properties of semimartingales

Abstract

The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry properties of both their ordinary as well as their stochastic logarithms. We provide a structure result for continuous quasi self-dual processes. Moreover, we give a characterisation of continuous Ocone martingales via a strong version of self-duality.