Differentiability of BSVIEs and Dynamic Capital Allocations
22 Pages Posted: 17 Jan 2014 Last revised: 3 Jun 2015
Date Written: June 2, 2015
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.
Keywords: Dynamic risk capital allocation, dynamic risk measure, backward stochastic Volterra integral equation, backward stochastic differential equation, gradient allocation, dynamic entropic risk measure
JEL Classification: D81
Suggested Citation: Suggested Citation