A varying terminal time mean-variance model

TL;DR

This paper introduces a novel mean-variance model with a dynamically changing terminal time and mean constraint, enhancing portfolio optimization by adapting to varying investment horizons.

Contribution

It proposes a new continuous-time mean-variance framework with a moving terminal time and mean constraint, using stochastic control techniques.

Findings

Optimal strategy and terminal time are derived analytically.

The model improves the efficient frontier in portfolio optimization.

Varying terminal time reduces portfolio variance.

Abstract

To improve the efficient frontier of the classical mean-variance model in continuous time, we propose a varying terminal time mean-variance model with a constraint on the mean value of the portfolio asset, which moves with the varying terminal time. Using the embedding technique from stochastic optimal control in continuous time and varying the terminal time, we determine an optimal strategy and related deterministic terminal time for the model. Our results suggest that doing so for an investment plan requires minimizing the variance with a varying terminal time.