A converse comparison theorem for bsdes and related properties of g-expectation

Abstract

In [1], Z. Chen proved that, if for each terminal condition ξ, the solution of the BSDE associated to the standard parameter (ξ, g1) is equal at time t = 0 to the solution of the BSDE associated to (ξ, g2) then we must have g1 ≡ g2. This result yields a natural question: what happens in the case of an inequality in place of an equality? In this paper, we try to investigate this question and we prove some properties of “g-expectation”, notion introduced by S. Peng in [8]. © 2000 Applied probability trust.