Representation of BSDE-Based Dynamic Risk Measures and Dynamic Capital Allocations
18 Pages Posted: 17 Jan 2014 Last revised: 27 Jun 2015
Date Written: March 14, 2014
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
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