Simulation of Coherent Risk Measures Based on Generalized Scenarios

Northwestern U. Industrial Engineering and Management Sciences Working Paper No. 05-002

36 Pages Posted: 1 Jun 2005

See all articles by Vadim Lesnevski

Vadim Lesnevski

Northwestern University - Department of Industrial Engineering and Management Sciences

Barry L. Nelson

Northwestern University - Department of Industrial Engineering and Management Sciences

Jeremy C. Staum

Northwestern University - Department of Industrial Engineering and Management Sciences

Date Written: October 3, 2006

Abstract

In financial risk management, coherent risk measures have been proposed as a way to avoid undesirable properties of measures such as value at risk that discourage diversifcation and do not account for the magnitude of the largest, and therefore most serious, losses. A coherent risk measure equals the maximum expected loss under several different probability measures, and these measures are analogous to populations or systems in the ranking-and-selection literature. However, here it is the value of the maximum expectation under any of the probability measures, and not the identity of the probability measure that attains it, that is of interest. We propose procedures to form fixed-width, simulation-based confidence intervals for a maximum of several expectations, explore their correctness and computational efficiency, and illustrate them on risk management problems. The availability of efficient algorithms for computing coherent risk measures will encourage their use for improved risk management.

Keywords: Coherent risk measures, good deal bounds, risk management, ranking and selection, simulation

Suggested Citation

Lesnevski, Vadim and Nelson, Barry L. and Staum, Jeremy C., Simulation of Coherent Risk Measures Based on Generalized Scenarios (October 3, 2006). Northwestern U. Industrial Engineering and Management Sciences Working Paper No. 05-002, Available at SSRN: https://ssrn.com/abstract=729663 or http://dx.doi.org/10.2139/ssrn.729663

Vadim Lesnevski (Contact Author)

Northwestern University - Department of Industrial Engineering and Management Sciences ( email )

Evanston, IL 60208-3119
United States

Barry L. Nelson

Northwestern University - Department of Industrial Engineering and Management Sciences ( email )

Evanston, IL 60208-3119
United States

Jeremy C. Staum

Northwestern University - Department of Industrial Engineering and Management Sciences ( email )

Evanston, IL 60208-3119
United States