Representation of BSDE-Based Dynamic Risk Measures and Dynamic Capital Allocations

18 Pages Posted: 17 Jan 2014 Last revised: 27 Jun 2015

See all articles by Eduard Kromer

Eduard Kromer

University of California, Berkeley

Ludger Overbeck

University of Giessen

Date Written: March 14, 2014

Abstract

In this short paper we provide a new representation result for dynamic capital allocations and dynamic convex risk measures that are based on backward stochastic differential equations. We derive this representation from a classical differentiability result for backward stochastic differential equations and the full allocation property of the Aumann-Shapley allocation. The representation covers BSDE-based dynamic convex and dynamic coherent risk measures. The results are applied to derive a representation for the dynamic entropic risk measure. Our result are also applicable in a specific way to the static case, where we are able to derive a new representation result for static convex risk measures that are Gateaux-differentiable.

Keywords: Dynamic risk measure, dynamic risk capital allocation, backward stochastic differential equation, gradient allocation, Aumann-Shaley allocation, dynamic entropic risk measure

JEL Classification: D81

Suggested Citation

Kromer, Eduard and Overbeck, Ludger, Representation of BSDE-Based Dynamic Risk Measures and Dynamic Capital Allocations (March 14, 2014). International Journal of Theoretical and Applied Finance, Vol. 17, No. 5, 2014, Available at SSRN: https://ssrn.com/abstract=2379523 or http://dx.doi.org/10.2139/ssrn.2379523

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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