The limitations of law-invariant insurance pricing

The limitations of law-invariant insurance pricing

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We show that a law-invariant pricing functional defined on a general Orlicz space is typically incompatible with frictionless risky assets in the sense that one and only one of the following two alternatives hold: either every risky payoff has a strictly-positive bid-ask spread, or the pricing functional is given by an expectation and hence every payoff has zero bid-ask spread. In doing so we extend and unify a variety of “collapse to the mean” results from the literature such as those obtained in [1] and [3], and we highlight the key role played by law invariance in determining such a collapse. As a byproduct, we derive several applications to law-invariant acceptance sets, risk measures and Schur-convex functionals. Finally, we discuss the relevance of these results in the framework of market-consistent pricing of insurances, as outlined in [2].

 

[1] Castagnoli, E., Maccheroni, F. and Marinacci, M. (2004), “Choquet insurance pricing: a caveat.” Mathematical Finance, vol. 14 (3), pp. 481-485.

[2] Dhaene, J., Stassen, B., Barigou, K., Linders, D. and Chen, Z. (2017), “Fair valuation of insurance liabilities: Merging actuarial judgement and market-consistency” Insurance: Mathematics and Economics, vol. 78, pp. 14-27.

[3] Frittelli, M. and Rosazza Gianin, E. (2005), “Law invariant convex risk measures.” Advances in Mathematical Economics, vol. 7, pp. 33-46.

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