Publication: Law-Invariant Functionals on General Spaces of Random Variables
Law-Invariant Functionals on General Spaces of Random Variables
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Bellini, F., Koch-Medina, P., Munari, C., & Svindland, G. (2021). Law-Invariant Functionals on General Spaces of Random Variables. SIAM Journal on Financial Mathematics, 12, 318–341. https://doi.org/10.1137/20m1341258
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We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large class of spaces of random variables. We sometimes obtain sharper versions, even for the well-studied case of bounded random variables. Our approach builds on two fundamental structural results for law-invariant functionals: the equivalence of law invariance and Schur convexity, i.e., monotonicity with respect to the convex stochastic order, and
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- Bellini, Fabio
- Munari, Cosimo
- Svindland, Gregor
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Bellini, F., Koch-Medina, P., Munari, C., & Svindland, G. (2021). Law-Invariant Functionals on General Spaces of Random Variables. SIAM Journal on Financial Mathematics, 12, 318–341. https://doi.org/10.1137/20m1341258
