# Semimartingale theory of monotone mean--variance portfolio allocation

## TL;DR

This paper develops a semimartingale framework for dynamic portfolio optimization under monotone mean-variance preferences, providing new insights into efficiency and the monotone Sharpe ratio.

## Contribution

It introduces a novel semimartingale approach to monotone mean-variance optimization and characterizes conditions for improving efficiency while maintaining non-negative cash flows.

## Key findings

- Characterization of when non-negative cash flows can be set aside without reducing efficiency
- Analysis of the monotone hull of the Sharpe ratio and its relevance
- Extension of previous work on mean-variance preferences in a general semimartingale setting

## Abstract

We study dynamic optimal portfolio allocation for monotone mean--variance preferences in a general semimartingale model. Armed with new results in this area we revisit the work of Cui, Li, Wang and Zhu (2012, MAFI) and fully characterize the circumstances under which one can set aside a non-negative cash flow while simultaneously improving the mean--variance efficiency of the left-over wealth. The paper analyzes, for the first time, the monotone hull of the Sharpe ratio and highlights its relevance to the problem at hand.