# Multivariate Optimized Certainty Equivalent Risk Measures and their Numerical Computation

arXiv: https://arxiv.org/abs/2210.13825 · HTML: https://mlsanity.com/paper/2210.13825/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2022.

## Built on by (most cited first, 1 of 1)

- [Optimized Certainty Equivalent Risk Minimization Using Samples: Algorithms, Convergence Rates, and Applications](https://mlsanity.com/paper/2608.07113/) (2026)

## Abstract (arXiv)

We present a framework for constructing multivariate risk measures that is inspired from univariate Optimized Certainty Equivalent (OCE) risk measures. We show that this new class of risk measures verifies the desirable properties such as convexity, monotonocity and cash invariance. We also address numerical aspects of their computations using stochastic algorithms instead of using Monte Carlo or Fourier methods that do not provide any error of the estimation.