Pricing financial derivatives by a minimizing method

TL;DR

This paper introduces a new numerical approach for solving backward stochastic differential equations, which are crucial in valuing financial derivatives in complete markets, by framing the solution as a minimization problem in a Banach space.

Contribution

It presents a novel method for establishing the existence of solutions to backward stochastic differential equations using a minimization framework.

Findings

New approach for solution existence in backward stochastic differential equations

Applicable to valuation of financial derivatives in complete markets

Facilitates numerical computations through minimization in Banach space

Abstract

We shall study backward stochastic differential equations and we will present a new approach for the existence of the solution. This type of equation appears very often in the valuation of financial derivatives in complete markets. Therefore, the identification of the solution as the unique element in a certain Banach space where a suitably chosen functional attains its minimum becomes interesting for numerical computations.