Log-optimal portfolio without NFLVR: existence, complete characterization, and duality

TL;DR

This paper develops a comprehensive theory for the existence, characterization, and duality of log-optimal portfolios in general semimartingale models without relying on the no-free-lunch-with-vanishing-risk condition, expanding applicability to models violating NFLVR.

Contribution

It provides a complete characterization and duality theory for log-optimal portfolios in models lacking NFLVR, including necessary and sufficient conditions for their existence.

Findings

Characterization of log-optimal portfolios without NFLVR

Necessary and sufficient conditions for portfolio existence

Duality results for optimal deflators

Abstract

This paper addresses the log-optimal portfolio for a general semimartingale model. The most advanced literature on the topic elaborates existence and characterization of this portfolio under no-free-lunch-with-vanishing-risk assumption (NFLVR). There are many financial models violating NFLVR, while admitting the log-optimal portfolio on the one hand. On the other hand, for financial markets under progressively enlargement of filtration, NFLVR remains completely an open issue, and hence the literature can be applied to these models. Herein, we provide a complete characterization of log-optimal portfolio and its associated optimal deflator, necessary and sufficient conditions for their existence, and we elaborate their duality as well without NFLVR.