On the semimartingale property via bounded logarithmic utility

TL;DR

This paper introduces a new criterion for establishing the semimartingale property in continuous stochastic processes using bounded logarithmic utility, providing a simplified proof and highlighting limitations in the discontinuous case.

Contribution

It offers a novel, self-contained condition for semimartingale characterization based on portfolio proportions, extending previous results and demonstrating their limitations in discontinuous models.

Findings

New criterion for semimartingale property in continuous processes

Simplified proof leveraging portfolio proportions

Counterexample showing limitations in discontinuous models

Abstract

This paper provides a new version of the condition of Di Nunno et al. (2003), Ankirchner and Imkeller (2005) and Biagini and \{O}ksendal (2005) ensuring the semimartingale property for a large class of continuous stochastic processes. Unlike our predecessors, we base our modeling framework on the concept of portfolio proportions which yields a short self-contained proof of the main theorem, as well as a counterexample, showing that analogues of our results do not hold in the discontinuous setting.