Set risk measures
Abstrak
We introduce the concept of set risk measures (SRMs), which are real-valued maps defined on the space of all non-empty, closed, and bounded sets of almost surely bounded random variables. Traditional risk measures typically operate on random variables, but SRMs extend this framework to sets of random variables. We establish an axiomatic scheme for SRMs, similar to classical risk measures but adapted for set operations. The main technical contribution is an axiomatic dual representation of convex SRMs by using regular, $τ$-additive (for nets) measures on the unit ball of the dual space of essentially bounded random variables. We explore worst-case SRMs, which evaluate risk as the supremum of individual risks within a set, and provide a collection of examples illustrating the applicability of our framework to systemic risk, optimization, and decision-making under uncertainty.
Penulis (3)
Marcelo Righi
Eduardo Horta
Marlon Moresco
Akses Cepat
- Tahun Terbit
- 2024
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓