Continuity properties of law-invariant (quasi-)convex risk functions on L ∞

We study continuity properties of law-invariant (quasi-)convex functions $${f:L^\infty(\Omega, \mathcal{F}, \mathbb{P}) \to (-\infty,\infty]}$$ over a non-atomic probability space $${(\Omega, \mathcal{F}, \mathbb{P})}$$. This is a supplementary note to Jouini etal. (Adv Math Econ 9:49-71, 2006

Brouwer’s Fan Theorem and Convexity

In the framework of Bishop’s constructive mathematics we introduce co-convexity as a property of subsets B of , the set of finite binary sequences, and prove that co-convex bars are uniform. Moreover, we establish a canonical correspondence between detachable subsets B of and uniformly continuous functions f defined on the unit interval such that B is a bar if and only if the corresponding function f is positive-valued, B is a uniform bar if and only if f has positive infimum, and B is co-convex if and only if f satisfies a weak convexity condition

Ambiguity sensitive preferences in Ellsberg frameworks

We study the market implications of ambiguity sensitive preferences using the α-maxmin expected utility (α-MEU) model. In the standard Ellsberg framework, we prove that α-MEU preferences are equivalent to either maxmin, maxmax or subjective expected utility (SEU). We show how ambiguity aversion impacts equilibrium asset prices, and revisit the laboratory experimental findings in Bossaerts et al. (Rev Financ Stud 23:1325–1359, 2010). Only when there are three or more ambiguous states, α-MEU, maxmin, maxmax and SEU models induce different portfolio choices. We suggest criteria to discriminate among these models in laboratory experiments and show that ambiguity seeking agents may prevent the existence of market equilibrium. Our results indicate that ambiguity matters for portfolio choice and does not wash out in equilibrium

Robust Optimal Risk Sharing and Risk Premia in Expanding Pools

We consider the problem of optimal risk sharing in a pool of cooperative agents. We analyze the asymptotic behavior of the certainty equivalents and risk premia associated with the Pareto optimal risk sharing contract as the pool expands. We first study this problem under expected utility preferences with an objectively or subjectively given probabilistic model. Next, we develop a robust approach by explicitly taking uncertainty about the probabilistic model (ambiguity) into account. The resulting robust certainty equivalents and risk premia compound risk and ambiguity aversion. We provide explicit results on their limits and rates of convergence, induced by Pareto optimal risk sharing in expanding pools

Subgradients of Law-Invariant Convex Risk Measures on L1

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