$L^2$-approximating pricing under restricted information

TL;DR

This paper develops a new approach to mean-variance hedging under limited information, introducing a novel martingale equation and linking it to backward stochastic differential equations to characterize optimal strategies.

Contribution

It introduces a new martingale equation for partial information hedging and connects it with backward stochastic differential equations, advancing the theoretical framework.

Findings

Characterization of optimal hedging strategies under restricted information.

Establishment of relations between the martingale equation and backward stochastic differential equations.

Theoretical insights into mean-variance hedging with incomplete information.

Abstract

We consider the mean-variance hedging problem under partial information in the case where the flow of observable events does not contain the full information on the underlying asset price process. We introduce a martingale equation of a new type and characterize the optimal strategy in terms of the solution of this equation. We give relations between this equation and backward stochastic differential equations for the value process of the problem.