# Computing expectiles via fixed point iterations

## TL;DR

This paper introduces fixed point iteration methods for computing expectiles, a class of risk measures in finance, providing new convergence proofs for these algorithms.

## Contribution

It offers a novel convergence proof for fixed point algorithms used to compute expectiles, enhancing their theoretical foundation.

## Key findings

- Fixed point characterizations enable efficient expectile computation
- Convergence of the algorithms is theoretically established
- Two-sided expectiles are practically computed using the proposed methods

## Abstract

Expectiles are statistical parameters which also provide a class of sublinear risk measures in finance. They are solutions of continuous optimization problems. The corresponding first order condition provides two different fixed point characterizations for expectiles, both of which can be utilized for computing them. Although especially the so-called two-sided version is already implemented and widely used, a general convergence proof appears to be new.