Continuous-time mean-variance portfolio selection under non-Markovian regime-switching model with random horizon

TL;DR

This paper develops a novel continuous-time mean-variance portfolio optimization framework incorporating non-Markovian regime-switching models with a random horizon, providing explicit solutions for optimal portfolios and the efficient frontier.

Contribution

It introduces a non-Markovian regime-switching model with predictable market parameters and derives closed-form solutions for the portfolio optimization problem with a random horizon.

Findings

Closed-form expressions for optimal portfolios.

Explicit characterization of the efficient frontier.

Extension to models with non-Markovian regime-switching and random horizon.

Abstract

In this paper, we consider a continuous-time mean-variance portfolio selection with regime-switching and random horizon. Unlike previous works, the dynamic of assets are described by non-Markovian regime-switching models in the sense that all the market parameters are predictable with respect to the filtration generated jointly by Markov chain and Brownian motion. We formulate this problem as a constrained stochastic linear-quadratic optimal control problem. The Markov chain is assumed to be independent of the Brownian motion. So the market is incomplete. We derive closed-form expressions for both the optimal portfolios and the efficient frontier. All the results are different from those in the problem with fixed time horizon.