TY - JOUR
T1 - Max-stable random sup-measures with comonotonic tail dependence
AU - Molchanov, Ilya
AU - Strokorb, Kirstin
PY - 2016/9/30
Y1 - 2016/9/30
N2 - Several objects in the Extremes literature are special instances of max-stable random sup-measures. This perspective opens connections to the theory of random sets and the theory of risk measures and makes it possible to extend corresponding notions and results from the literature with streamlined proofs. In particular, it clarifies the role of Choquet random sup-measures and their stochastic dominance property. Key tools are the LePage representation of a max-stable random sup-measure and the dual representation of its tail dependence functional. Properties such as complete randomness, continuity, separability, coupling, continuous choice, invariance and transformations are also analysed.
AB - Several objects in the Extremes literature are special instances of max-stable random sup-measures. This perspective opens connections to the theory of random sets and the theory of risk measures and makes it possible to extend corresponding notions and results from the literature with streamlined proofs. In particular, it clarifies the role of Choquet random sup-measures and their stochastic dominance property. Key tools are the LePage representation of a max-stable random sup-measure and the dual representation of its tail dependence functional. Properties such as complete randomness, continuity, separability, coupling, continuous choice, invariance and transformations are also analysed.
UR - https://www.scopus.com/pages/publications/84979724833
U2 - 10.1016/j.spa.2016.03.004
DO - 10.1016/j.spa.2016.03.004
M3 - Article
SN - 0304-4149
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
ER -