Differentiability of BSVIEs and Dynamic Capital Allocations

22 Pages Posted: 17 Jan 2014 Last revised: 3 Jun 2015

See all articles by Eduard Kromer

Eduard Kromer

University of California, Berkeley

Ludger Overbeck

University of Giessen

Date Written: June 2, 2015

Abstract

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

Kromer, Eduard and Overbeck, Ludger, Differentiability of BSVIEs and Dynamic Capital Allocations (June 2, 2015). Available at SSRN: https://ssrn.com/abstract=2379500 or http://dx.doi.org/10.2139/ssrn.2379500

Eduard Kromer (Contact Author)

University of California, Berkeley ( email )

Evans Hall
Berkeley, CA 3860 94720
United States

Ludger Overbeck

University of Giessen ( email )

Institut of Mathematics
Giessen, 35394
Germany

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