Continuous-Time Monotone Mean-Variance Portfolio Selection in Jump-Diffusion Model

TL;DR

This paper derives an explicit solution for continuous-time portfolio optimization using monotone mean-variance preferences in jump-diffusion models, addressing issues of non-monotonicity and free cash flow problems present in classical mean-variance approaches.

Contribution

It introduces a novel explicit solution for MMV preferences in jump-diffusion models, demonstrating their advantages over classical MV and establishing foundational theoretical results.

Findings

MMV preferences can be restricted to non-negative Doléans-Dade exponentials.

MMV resolves non-monotonicity and free cash flow issues in MV models.

Validation of two-fund separation and monotone CAPM for MMV investors.

Abstract

We study continuous-time portfolio selection under monotone mean-variance (MMV) preferences in a jump-diffusion model, presenting an explicit solution different from that under classical mean-variance (MV) preferences in dynamic settings for the first time. We prove that the potential measures calculating MMV preferences can be restricted to non-negative Dol\'eans-Dade exponentials. We find that MMV can resolve the non-monotonicity and free cash flow stream problems of MV when the jump size can be larger than the inverse of the market price of risk. Such result is completely comparable to the earliest result by Dybvig and Ingersoll. Economically, we show that the essence of MMV lies in the pricing operator always remaining non-negative, with a value of zero assigned when the jump exceeds a certain threshold, avoiding the issue of non-monotonicity. As a result, MMV investors behave markedly different from MV investors. Furthermore, we validate the two-fund separation and establish the monotone capital asset pricing model (monotone CAPM) for MMV investors. We also study MMV in a constrained trading model and provide three specific numerical examples to show MMV's efficiency. Our finding can serve as a crucial theoretical foundation for future empirical tests of MMV and monotone CAPM's effectiveness.