A Converse Comparison Theorem for BSDEs and Related Properties of g-Expectation

Abstract

In [1], Z. Chen proved that, if for each terminal condition $\xi$, the solution of the BSDE associated to the standard parameter $(\xi, g_1)$ is equal at time $t=0$ to the solution of the BSDE associated to $(\xi, g_2)$ then we must have $g_1\equiv g_2$. 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].