Prof. Dr. Ludger Overbeck

Capital allocations have been studied in conjunction with static risk measures in various papers. The dynamic case has been studied only in a discrete-time setting. We address the problem of allocating risk capital to subportfolios in a continuous- time dynamic context. For this purpose we introduce a classical differentiability result for backward stochastic Volterra integral equations and apply this result to derive continuous-time dynamic capital allocations. Moreover, we study a dynamic capital allocation principle that is based on backward stochastic differential equations and derive the dynamic gradient allocation for the dynamic entropic risk measure. As a consequence we finally provide a representation result for dynamic risk measures that is based on the full allocation property of the Aumann-Shapley allocation, which is also new in the static case