We consider an incomplete market with two information structures, complete and partial information $\bb F$ and $\bb G$ respectively. The dynamics of the market are given by a risky asset driven by a $m$-dimensional Brownian motion $W=(W_1,\cdots,W_m)'$ as well as an integer-valued random measure $\mu(du,dy)$. To study the values with respect to the different information filtrations, we introduce the concept of \emph{dynamic $\exp$-utility indifference value (UIV) of $\bb F$ with respect to $\bb G$} denoted by $C_t$ and the concept of \emph{dynamic $(\bb F,\bb G)$ $\exp$-UIV of the contingent claim $H$} denoted by $C_t(H)$, and we describe the dynamics of $C_t$ and $C_t(H)$ by BSDEs.