Representation and approximation of convex dynamic risk measures with respect to strong-weak topologies

Okhrati, Ramin and Assa, Hirbod (2017) Representation and approximation of convex dynamic risk measures with respect to strong-weak topologies. STOCHASTIC ANALYSIS AND APPLICATIONS, 35 (4). pp. 604-614.

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Official URL: http://dx.doi.org/10.1080/07362994.2017.1289104

Abstract

We provide a representation for strong-weak continuous dynamic risk measures from Lp into Lpt spaces where these spaces are equipped respectively with strong and weak topologies and p is a finite number strictly larger than one. Conversely, we show that any such representation that admits a compact (with respect to the product of weak topologies) sub-differential generates a dynamic risk measure that is strong--weak continuous. Furthermore, we investigate sufficient conditions on the sub-differential for which the essential supremum of the representation is attained. Finally, the main purpose is to show that any convex dynamic risk measure that is strong-weak continuous can be approximated by a sequence of convex dynamic risk measures which are strong--weak continuous and admit compact sub-differentials with respect to the product of weak topologies. Throughout the arguments, no conditional translation invariance or monotonicity assumptions are applied.

Item Type:	Article
Depositing User:	Symplectic Admin
Date Deposited:	05 Dec 2018 16:18
Last Modified:	19 Jan 2023 01:09
DOI:	10.1080/07362994.2017.1289104
Open Access URL:	https://eprints.soton.ac.uk/399165/2/Manuscript.pd...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3029579