Multivariate Optimized Certainty Equivalent Risk Measures and their Numerical Computation

TL;DR

This paper introduces a new class of multivariate risk measures based on univariate OCE, ensuring key properties and offering stochastic algorithms for accurate numerical computation.

Contribution

It develops a novel multivariate risk measure framework inspired by univariate OCE and proposes stochastic algorithms for its numerical estimation.

Findings

Risk measures are convex, monotone, and cash-invariant.

Stochastic algorithms provide error-controlled numerical computation.

Framework extends univariate OCE to multivariate settings.

Abstract

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.