Data and Uncertainty in Extreme Risks: A Nonlinear Expectations Approach

Samuel N. Cohen

Chapter 6 in Innovations in Insurance, Risk- and Asset Management:Proceedings of the Innovations in Insurance, Risk- and Asset Management Conference, 2018, pp 135-162 from World Scientific Publishing Co. Pte. Ltd.

Abstract: Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [1], can assist in the quantification of statistical uncertainty for these problems. However, when we are in a heavy-tailed context (in particular when our data are described by a Pareto distribution, as is common in much of extreme value theory), the theory of [1] is insufficient, and requires an additional regularization step which we introduce. By asking whether this regularization is possible, we obtain a qualitative requirement for reliable estimation of tail quantities and risk measures, in a Pareto setting.

Keywords: Insurance; Actuarial Science; Risk Measure; Reinsurance; Copula; Replicating Portfolio; Bayesian Finance; Risk Classification; Stochastic Dominance; Dynamic Hedging; Autoregressive Hidden Markov Models; Exchange-Traded Funds; Uncertainty Quantification; Fixed Income; Stochastic Processes for Finance (search for similar items in EconPapers)
JEL-codes: G22 G32 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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