  In this paper, we provide a representation theorem for dynamic capital
allocation under It{\^o}-L{\'e}vy model. We consider the representation of
dynamic risk measures defined under Backward Stochastic Differential Equations
(BSDE) with generators that grow quadratic-exponentially in the control
variables. Dynamic capital allocation is derived from the differentiability of
BSDEs with jumps. The results are illustrated by deriving a capital allocation
representation for dynamic entropic risk measure and static coherent risk
measure.
