For monotone cash-additive risk measures on Orlicz spaces, unexpected loss convergence under weighted WLLN plus UI equals scalar continuity at origin; homogeneous cases yield o(n lambda_bar_n) losses with analogous Choquet and risk-ratio results.
Namioka.Partially ordered linear topological spaces, volume 24 ofMem
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Asymptotic Behaviour of Unexpected Losses and Risk Ratios for Co-Monotonic Alternatives
For monotone cash-additive risk measures on Orlicz spaces, unexpected loss convergence under weighted WLLN plus UI equals scalar continuity at origin; homogeneous cases yield o(n lambda_bar_n) losses with analogous Choquet and risk-ratio results.