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We study continuity properties of law-invariant (quasi-)convex functions f : L1(Ω,F, P) to ( ∞,∞] over a non-atomic probability space (Ω,F, P) .This is a supplementary note to [12] ...
We introduce a generalised subgradient for law-invariant closed convex risk measures on L1 and establish its relationship with optimal risk allocations and equilibria. Our main result gives sufficient conditions ensuring a non-empty generalised subgradient ...
We investigate the problem of optimal risk sharing between agents endowed with cash-invariant choice functions which are law-invariant with respect to different reference probability measures. We motivate a discrete setting both from an operational and a t ...
Recently Heyde, Kou and Peng (2007) proposed the notion of a natural risk statistic associated with a finite sample that relaxes the subadditivity assumption in the classical coherent risk statistics. In this note we use convex analysis to provide alternat ...
We prove the existence of comonotone Pareto optimal allocations satisfying utility constraints when decision makers have probabilistic sophisticated variational preferences and thus representing criteria in the class of law invariant robust utilities. The ...
We prove the existence of Pareto optimal allocations within sets of acceptable allocations when decision makers have probabilistic sophisticated variational preferences defined on random endowments in L1. ...
Springer Verlag2013
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In this paper, we establish a one-to-one correspondence between law-invariant convex risk measures on L8 and L1. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L1. ...
Wiley-Blackwell2012
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In this paper we provide the complete solution to the existence and characterization problem of optimal capital and risk allocations for not necessarily monotone, law-invariant convex risk measures on the model space Lp, for any p ε [1;∞]. Our main result ...
Springer Verlag2008
We study monotone convex functions psi : L-0 (Omega, F, P) -> (-infinity, infinity] and derive a dual representation as well as conditions that ensure the existence of a sigma-additive subgradient. The results are motivated by applications in economic agen ...
