REPRESENTATION OF BSDE-BASED DYNAMIC RISK MEASURES AND DYNAMIC CAPITAL ALLOCATIONS

Eduard Kromer () and Ludger Overbeck ()
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Eduard Kromer: Department of Mathematics, University of Gießen, Gießen 35390, Germany
Ludger Overbeck: Department of Mathematics, University of Gießen, Gießen 35390, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 05, 1-16

Abstract: In this paper, we provide a new representation result for dynamic capital allocations and dynamic convex risk measures that are based on backward stochastic differential equations (BSDEs). We derive this representation from a classical differentiability result for BSDEs 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 results 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 Gâteaux-differentiable.

Keywords: Dynamic risk measure; dynamic risk capital allocation; backward stochastic differential equation; gradient allocation; Aumann–Shaley allocation; dynamic entropic risk measure (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S0219024914500320

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