Estimation of Spectral Risk Measures
This work addresses risk assessment in fields like finance and engineering, but it is incremental as it builds on existing spectral risk measure theory with specific distributional assumptions.
The paper tackles the problem of estimating spectral risk measures from independent and identically distributed samples by proposing a novel method based on numerical integration, showing that the estimate concentrates exponentially for distributions with bounded support and deriving bounds for Gaussian or exponential distributions, with validation on synthetic and vehicular traffic routing applications.
We consider the problem of estimating a spectral risk measure (SRM) from i.i.d. samples, and propose a novel method that is based on numerical integration. We show that our SRM estimate concentrates exponentially, when the underlying distribution has bounded support. Further, we also consider the case when the underlying distribution is either Gaussian or exponential, and derive a concentration bound for our estimation scheme. We validate the theoretical findings on a synthetic setup, and in a vehicular traffic routing application.