Stratonovich representation of semimartingale rank processes

TL;DR

This paper presents a novel Stratonovich integral representation for semimartingale rank processes, enabling new decompositions of portfolio log-returns based on ranked market weights.

Contribution

It introduces a generalized Stratonovich integral framework for continuous semimartingale rank processes, facilitating advanced financial portfolio analysis.

Findings

Rank processes can be represented by generalized Stratonovich integrals.

The representation allows decomposition of relative log-returns of rank-based portfolios.

Applicable to reversible semimartingales with nondegenerate crossings.

Abstract

Suppose that $X_1, \ldots , X_n$ are continuous semimartingales that are reversible and have nondegenerate crossings. Then the corresponding rank processes can be represented by generalized Stratonovich integrals, and this representation can be used to decompose the relative log-return of portfolios generated by functions of ranked market weights.