DIFFERENTIABILITY OF BSVIEs AND DYNAMIC CAPITAL ALLOCATIONS

Eduard Kromer () and Ludger Overbeck ()
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Eduard Kromer: Department of Mathematics, University of Gießen, Gießen 35392, Germany
Ludger Overbeck: Department of Mathematics, University of Gießen, Gießen 35392, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2017, vol. 20, issue 07, 1-26

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 for the first time in a continuous-time dynamic context. For this purpose, we introduce a 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; Aumann–Shapley allocation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024917500479

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