BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets

TL;DR

This paper studies infinite-dimensional BSDEs driven by cylindrical martingales, establishing existence, uniqueness, and approximation results, and applies these findings to develop converging hedging strategies in bond markets.

Contribution

It introduces a framework for solving infinite-dimensional BSDEs driven by cylindrical martingales and applies it to approximate hedging in bond markets.

Findings

Existence and uniqueness of solutions for infinite-dimensional BSDEs.

Finite-dimensional BSDE solutions approximate the infinite-dimensional solution.

Locally risk-minimizing strategies converge to the generalized hedge.

Abstract

We consider Lipschitz-type backward stochastic differential equations (BSDEs) driven by cylindrical martingales on the space of continuous functions. We show the existence and uniqueness of the solution of such infinite-dimensional BSDEs and prove that the sequence of solutions of corresponding finite-dimensional BSDEs approximates the original solution. We also consider the hedging problem in bond markets and prove that, for an approximately attainable contingent claim, the sequence of locally risk-minimizing strategies based on small markets converges to the generalized hedging strategy.