A New Coherent Multıvariate Average-Value-at-Risk

Abstract: A new operator for handling the joint risk of different sources has been presented and its various properties are investigated. The problem of risk evaluation of multivariate risk sources has been studied, and a multivariate risk measure, the so-called multivariate average-value-at-risk, mAVaRα, is proposed to quantify the total risk. It is shown that the proposed operator satisfies the four axioms of a coherent risk measure while reducing to one variable average-value-at-risk, AVaRα, in case N = 1. In that respect, it is shown that mAVaRα is the natural extension of AVaRα to the N-dimensional case maintaining its axiomatic properties. The framework is applicable for Gaussian mixture models with dependent risk factors that are naturally used in financial and actuarial modeling. Examples of numerical simulations are also illustrated throughout.

Speaker Biography: Kerem Uğurlu finished his Ph.D. in Applied Mathematics at the University of Southern California in 2016. Between 2016-2018, he worked as a postdoctoral research associate at the Department of Applied Mathematics, University of Washington. In 2019, he worked as a data scientist in Singapore. Since August 2019, he has been working at Nazarbayev University, Kazakhstan, as an assistant professor of mathematics. His research interests are stochastic analysis, mathematical statistics, and its applications.