scholarly journals A new view on risk measures associated with acceptance sets

2011 ◽  
Author(s):  
Walter Farkas ◽  
Pablo Koch Medina ◽  
Cosimo-Andrea Munari

2018 ◽  
Vol 29 (1) ◽  
pp. 329-367 ◽  
Author(s):  
Francesca Biagini ◽  
Jean-Pierre Fouque ◽  
Marco Frittelli ◽  
Thilo Meyer-Brandis

2020 ◽  
Vol 45 (4) ◽  
pp. 1342-1370 ◽  
Author(s):  
Niushan Gao ◽  
Cosimo Munari

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.


1995 ◽  
Vol 40 (4) ◽  
pp. 384-385
Author(s):  
Terri Gullickson
Keyword(s):  

1991 ◽  
Vol 36 (10) ◽  
pp. 839-840
Author(s):  
William A. Yost
Keyword(s):  

2000 ◽  
Author(s):  
Patrick DeLeon ◽  
Keyword(s):  

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