On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation

Dilip Madan, Martijn Pistorius and Mitja Stadje ()

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Abstract: In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk-measures in terms of certain backward stochastic differential equations. By establishing a functional limit theorem, we show that DSRs may be considered to be (strongly) time-consistent continuous-time extensions of iterated spectral risk-measures, which are obtained by iterating a given spectral risk-measure (such as Expected Shortfall) along a given time-grid. Specifically, we demonstrate that any DSR arises in the limit of a sequence of such iterated spectral risk-measures driven by lattice-random walks, under suitable scaling and vanishing time- and spatial-mesh sizes. To illustrate its use in financial optimisation problems, we analyse a dynamic portfolio optimisation problem under a DSR.

Date: 2013-01, Revised 2017-04
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1301.3531

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