In this paper coherent risk measures and other currently used risk measures, notably Value-at-Risk (VaR), are studied from the perspective of the theory of coherent imprecise previsions. We show that coherent risk measures are a special case of coherent upper previsions and extend their definition and several properties to arbitrary sets of risks. We also prove that Value-at-Risk does not necessarily satisfy a weaker notion of coherence called Avoiding Sure Loss (ASL), and discuss both sufficient conditions for VaR to be ASL and ways of modifying VaR into a coherent risk measure.
Keywords. Coherent risk measure, imprecise prevision, Value-at-Risk, Avoiding Sure Loss condition
Format. PDF
Paper Download
The paper is availabe in the following sites:
Authors addresses:
Renato Pelessoni
Renato Pelessoni
Dipartimento di Matematica applicata 'B. de Finetti'
Facolta' di Economia
Universita' di Trieste
Piazzale Europa, 1
I - 34127 Trieste, Italy
Paolo Vicig
Paolo Vicig
Dipartimento di Matematica applicata 'B. de Finetti'
Facolta' di Economia
Universita' di Trieste
Piazzale Europa, 1
I - 34127 Trieste, Italy
E-mail addresses:
| Renato Pelessoni | renatop@econ.univ.trieste.it |
| Paolo Vicig | paolov@econ.univ.trieste.it |