A comonotonic theorem for backward stochastic differential equations in $L^p$ and its applications

Abstract

We study backward stochastic differential equations (BSDEs) under weak assumptions on the data. We obtain a comonotonic theorem for BSDEs in $L^p,\quad 1, 1 < p ≤ 2$. As applications of this theorem, we study the relation between Choquet expectations and minimax expectations and the relation between Choquet expectations and generalized Peng’s $g$-expectations. These results generalize the known results of Chen et al.