BSDEs under partial information and financial applications

TL;DR

This paper establishes existence and uniqueness of solutions for backward stochastic differential equations (BSDEs) driven by general martingales under partial information, with applications to financial risk management.

Contribution

It introduces new results for BSDEs under partial information and connects solutions to full information cases, including a partial information Föllmer-Schweizer decomposition.

Findings

Existence and uniqueness of BSDE solutions under partial information

Derivation of partial information Föllmer-Schweizer decomposition

Application to local risk-minimization in financial markets

Abstract

In this paper we provide existence and uniqueness results for the solution of BSDEs driven by a general square integrable martingale under partial information. We discuss some special cases where the solution to a BSDE under restricted information can be derived by that related to a problem of a BSDE under full information. In particular, we provide a suitable version of the F\"ollmer-Schweizer decomposition of a square integrable random variable working under partial information and we use this achievement to investigate the local risk-minimization approach for a semimartingale financial market model.