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

A note on representation of BSDE-based dynamic risk measures and dynamic capital allocations