  There has been a renewed interest in exponential concentration inequalities
for stochastic processes in probability and statistics over the last three
decades. De la Pe\~{n}a \cite{d} establishes a nice exponential inequality for
discrete time locally square integrable martingale . In this paper, we obtain
de la Pe\~{n}a's inequalities for stochastic integral of multivariate point
processes. The proof is primarily based on Dol\'{e}ans-Dade exponential formula
and the optional stopping theorem. As application, we obtain an exponential
inequality for block counting process in $\Lambda-$coalescents.
