# On mean-variance hedging under partial observations and terminal wealth constraints

## TL;DR

This paper addresses mean-variance hedging with partial observations and terminal wealth constraints, proposing a new martingale representation-based solution applicable to square-integrable semimartingales, with explicit solutions in special cases.

## Contribution

It introduces a novel approach to solve mean-variance hedging problems under incomplete information using martingale representation, including explicit solutions via Clark-Ocone in certain cases.

## Key findings

- Solution provided for square-integrable semimartingale models
- Explicit solutions obtained using Clark-Ocone representation in special cases
- Illustrated with an example involving two correlated geometric Brownian motions

## Abstract

In the paper, a mean-square minimization problem under terminal wealth constraint with partial observations is studied. The problem is naturally connected to the mean-variance hedging problem under incomplete information. A new approach to solving this problem is proposed. The paper provides a solution when the underlying pricing process is a square-integrable semimartingale. The proposed method for the study is based on the martingale representation. In special cases, the Clark-Ocone representation can be used to obtain explicit solutions. The results and the method are illustrated and supported by example with two correlated geometric Brownian motions.