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

TL;DR

This paper investigates how the risk premium behaves as the number of risks in a large pool increases, revealing a slower convergence rate influenced by specific risk preferences.

Contribution

It provides an asymptotic analysis of risk premia under law-invariant risk measures, including rank-dependent utility, in large risk sharing pools.

Findings

Convergence rate of risk premium is typically n^{1/2}

Behavior depends on the specific risk preferences

Analysis applies to a broad class of law-invariant risk measures

Abstract

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