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Contribution Details

Type Journal Article
Scope Discipline-based scholarship
Title Surplus-invariant risk measures
Organization Unit
  • Niushan Gao
  • Cosimo Munari
Item Subtype Original Work
Refereed Yes
Status Published in final form
  • English
Journal Title Mathematics of operations research
Publisher Institute for Operations Research and the Management Sciences (I N F O R M S)
Geographical Reach international
ISSN 0364-765X
Volume 45
Number 4
Page Range 1342 - 1370
Date 2020
Abstract Text This paper presents a systematic study of the notion of surplus invariance, which plays a natural and important role in the theory of risk measures and capital requirements. So far, this notion has been investigated in the setting of some special spaces of random variables. In this paper, we develop a theory of surplus invariance in its natural framework, namely, that of vector lattices. Besides providing a unifying perspective on the existing literature, we establish a variety of new results including dual representations and extensions of surplus-invariant risk measures and structural results for surplus-invariant acceptance sets. We illustrate the power of the lattice approach by specifying our results to model spaces with a dominating probability, including Orlicz spaces, as well as to robust model spaces without a dominating probability, where the standard topological techniques and exhaustion arguments cannot be applied.
Digital Object Identifier 10.1287/moor.2019.1035
Other Identification Number merlin-id:19872
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