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We analyze the limiting behavior of the risk premium associated with thePareto optimal risk sharing contract in an infinitely expanding pool of risksunder a general class of law-invariant risk measures encompassingrank-dependent utility preferences. We show that the corresponding convergencerate is typically only $n^{1/2}$ instead of the conventional $n$, with $n$ themultiplicity of risks in the pool, depending upon the precise risk preferences.

Asymptotic Analysis of Risk Premia Induced by Law-Invariant Risk Measures