A new comparison theorem of multidimensional BSDEs

TL;DR

This paper introduces a new total order on R^N and uses it with backward stochastic viability to establish a necessary and sufficient comparison theorem for multidimensional BSDEs in financial markets.

Contribution

It presents a novel total order on R^N and derives a new comparison theorem for multidimensional BSDEs using this order.

Findings

Established a new total order on R^N.

Derived necessary and sufficient conditions for comparison of multidimensional BSDEs.

Applied the results to contingent claim pricing in no-arbitrage markets.

Abstract

In this paper, we define a new total order on R^N and use this order together with backward stochastic viability property(for short BSVP) to study the property of the generator of backward stochastic differential equation(for short BSDE) when the price of contingent claim can be represented by a BSDE in the no-arbitrage financial market. The main result is the necessary and sufficient condition for comparison theorem of multidimensional BSDEs under this order.