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A note on representation of BSDE-based dynamic risk measures and dynamic capital allocations (1808.04611v1)
Published 14 Aug 2018 in q-fin.PM, math.ST, and stat.TH
Abstract: 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.