# Mean-variance portfolio selection under partial information with drift uncertainty

## TL;DR

This paper addresses mean-variance portfolio optimization under partial information with uncertain drift, deriving optimal strategies via backward stochastic differential equations and proposing an efficient numerical approximation scheme.

## Contribution

It demonstrates market completeness despite partial information and drift uncertainty, and introduces a novel numerical method using Malliavin calculus and particle representation.

## Key findings

- Optimal strategy derived from BSDEs under partial information
- Market remains complete despite drift uncertainty
- Proposed numerical scheme effectively approximates the optimal portfolio

## Abstract

In this paper, we study the mean-variance portfolio selection problem under partial information with drift uncertainty. First we show that the market model is complete even in this case while the information is not complete and the drift is uncertain. Then, the optimal strategy based on partial information is derived, which reduces to solving a related backward stochastic differential equation (BSDE). Finally, we propose an efficient numerical scheme to approximate the optimal portfolio that is the solution of the BSDE mentioned above. Malliavin calculus and the particle representation play important roles in this scheme.