Continuous-time Mean-Variance Portfolio Selection with Stochastic Parameters

TL;DR

This paper develops a continuous-time mean-variance portfolio optimization model with stochastic parameters influenced by Gaussian economic factors, addressing partial information and deriving explicit optimal strategies.

Contribution

It introduces a novel partial-information control framework for stochastic mean-variance portfolio selection with explicit solutions involving Riccati and linear ODEs.

Findings

Optimal portfolio strategies are explicitly derived.

The model accounts for unobservable economic factors.

Solutions involve solving Riccati and linear backward ODEs.

Abstract

This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a bond. In the considered model firstly proposed by [3], the mean returns of individual assets are explicitly affected by underlying Gaussian economic factors. Using past and present information of the asset prices, a partial-information stochastic optimal control problem with random coefficients is formulated. Here, the partial information is due to the fact that the economic factors can not be directly observed. Via dynamic programming theory, the optimal portfolio strategy can be constructed by solving a deterministic forward Riccati-type ordinary differential equation and two linear deterministic backward ordinary differential equations.