Convex Risk Measures Beyond Bounded Risks, or The Canonical Model Space for Law-Invariant Convex Risk Measures is L^1
نویسندگان
چکیده
In this paper we provide a rigorous toolkit for extending convex risk measures from L∞ to L, for p ≥ 1. Our main result is a one-to-one correspondence between law-invariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L. Some significant counterexamples illustrate the many pitfalls with convex risk measures and their extensions to L.
منابع مشابه
Convex Risk Measures Beyond Bounded Risks
This work addresses three main issues: Firstly, we study the interplay of risk measures on L∞ and Lp, for p ≥ 1. Our main result is a one-to-one correspondence between law-invariant closed convex risk measures on L∞ and L1. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L1. Secondly, we provide the solution to the existence and char...
متن کاملThe Canonical Model Space for Law - invariant Convex Risk Measures is L 1 ∗
In this paper we establish a one-to-one correspondence between lawinvariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L.
متن کاملThe Canonical Model Space for Law-invariant
In this paper we establish a one-to-one correspondence between lawinvariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L.
متن کاملOptimal capital and risk allocations for law- and cash-invariant convex functions
In this paper we provide the complete solution to the existence and characterisation problem of optimal capital and risk allocations for not necessarily monotone, law-invariant convex risk measures on the model space L, for any p ∈ [1,∞]. Our main result says that the capital and risk allocation problem always admits a solution via contracts whose payoffs are defined as increasing Lipschitz con...
متن کاملOn convex risk measures on Lp-spaces
Much of the recent literature on risk measures is concerned with essentially bounded risks in L∞. In this paper we investigate in detail continuity and representation properties of convex risk measures on L spaces. This frame for risks is natural from the point of view of applications since risks are typically modelled by unbounded random variables. The various continuity properties of risk mea...
متن کامل