Simulation of Coherent Risk Measures Based on Generalized Scenarios

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

Working Paper Series