Data and uncertainty in extreme risks - a nonlinear expectations\n approach

2017/05/23 by Samuel N. Cohen, Cohen, Samuel N.
Decision Sciences · Economics, Econometrics and Finance · Engineering · #60A86 #62F86 #62G32 #91G70 #FOS: Economics and business #FOS: Mathematics #Monetary Policy and Economic Impact #Probability (math.PR) #Reservoir Engineering and Simulation Methods #Risk and Portfolio Optimization #Statistical Finance (q-fin.ST) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1705.08301

openalex publication_date 2017/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Estimation of tail quantities, such as expected shortfall or Value at Risk,\nis a difficult problem. We show how the theory of nonlinear expectations, in\nparticular the Data-robust expectation introduced in [5], can assist in the\nquantification of statistical uncertainty for these problems. However, when we\nare in a heavy-tailed context (in particular when our data are described by a\nPareto distribution, as is common in much of extreme value theory), the theory\nof [5] is insufficient, and requires an additional regularization step which we\nintroduce. By asking whether this regularization is possible, we obtain a\nqualitative requirement for reliable estimation of tail quantities and risk\nmeasures, in a Pareto setting.\n

Related

• Extreme expectile estimation for short-tailed data, with an application to market risk assessment
• Propagation of Input Tail Uncertainty in Rare-Event Estimation: A Light versus Heavy Tail Dichotomy
• Improved inference on risk measures for univariate extremes
• Range Value-at-Risk: Multivariate and Extreme Values
• Tail risk inference via expectiles in heavy-tailed time series