A new comparison theorem of multidimensional BSDEs

Abstract

In this paper, we first study a property about the generator g of Backward Stochastic Differential Equation (BSDE) when the price of contingent claims can be represented by a multidimensional BSDE in the no-arbitrage financial market. Furthermore, motivated by the behavior of agents in finance market, we introduce a new total order on ℝ n and obtain a necessary and sufficient condition for comparison theorem of multidimensional BSDEs under this order. We also give some further results for .