Abstract

A spectral risk measure (SRM) is a weighted average of value at risk where the weighting function (also known as risk spectrum or distortion function) characterizes a decision maker's risk attitude. In this paper, we consider the case where the decision maker's risk spectrum is ambiguous and introduce a robust SRM model based on the worst risk spectrum from a ball of risk spectra centered at a nominal risk spectrum. When the ball consists of step-like risk spectra, we show that the robust SRM can be computed by solving a linear programming problem. For the general case, we propose a step-like approximation scheme and derive an error bound for the approximation. As an application, we apply the proposed robust SRM to one-stage stochastic optimization with the objective of minimizing the robust SRM and propose an alternating iterative algorithm for solving the resulting minimax optimization problem. Moreover, to examine stability of the robust spectral risk optimization model with respect to perturbation of observed data from the underlying exogenous uncertainty in data-driven environments, we investigate statistical robustness of the model and derive sufficient conditions for the required stability.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.