Robust optimized certainty equivalents and quantiles for loss positions with distribution uncertainty

Zixin Feng; Weiwei Li; Dejian Tian

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arXiv · 2304.04396

Robust optimized certainty equivalents and quantiles for loss positions with distribution uncertainty

Zixin Feng·Weiwei Li·Dejian Tian

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Abstract

This paper investigates the robust optimized certainty equivalents and analyzes their properties as risk measures under distribution uncertainty. Building on this, robust generalized quantiles are proposed and discussed. We then consider robust expectiles with two specific penalization functions. For the one with a linear penalization function, it is proved to be a coherent risk measure and its dual representation is provided. Furthermore, numerical simulations are conducted to examine the effect of the penalization functions on the robust expectiles and to compare them with classical expectiles.

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Zixin Feng, Weiwei Li, Dejian Tian. 2023-04-10. Robust optimized certainty equivalents and quantiles for loss positions with distribution uncertainty. https://arxiv.org/abs/2304.04396

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