Numerical Solution of a parabolic problem arising in finance

TL;DR

This paper addresses the numerical computation of optimal replication strategies in incomplete financial markets by analyzing a PDE system, establishing solution existence and uniqueness, and proposing a numerical method.

Contribution

It introduces a new numerical approach for solving PDE systems related to financial replication strategies, with theoretical guarantees.

Findings

Proved existence and uniqueness of solutions in Sobolev spaces

Developed a numerical method for PDE system

Validated the method with computational experiments

Abstract

The optimal replication strategy for incomplete markets is obtained by solving a system of partial differential equations. In this paper, we study existence and uniqueness of the solution in suitable Sobolev spaces and propose a numerical method to compute the optimal strategy