Optimization of conditional value-at-risk. Reliability Engineering & System Safety, 95, 499–510. On buffered failure probability in design and optimization of structures. Maximization of AUC and buffered AUC in binary classification. The Journal of Machine Learning Research, 18(1), 2285–2327. Soft margin support vector classification as buffered probability minimization. Buffered probability of exceedance: Mathematical properties and optimization. European Journal of Operational Research, 270(3), 826–836. Estimation and asymptotics for buffered probability of exceedance. Mafusalov, A., Shapiro, A., & Uryasev, S. North American Actuarial Journal, 7(4), 55–71. Tail conditional expectation for elliptical distributions. Communications in Statistics: Simulation and Computation, 28(3), 793–819. Fitting the generalized lambda distribution to data: A method based on percentiles. Analysis of tropical storm damage using buffered probability of exceedance. Helsinki School of Economics working paper W-389.Īrtzner, P., Delbaen, F., Eber, J. With the freedom to select various combinations of confidence levels, MOS allows the user to focus the fitting procedure on different portions of the distribution, such as the tail when fitting heavy-tailed asymmetric data.Īndreev, A., Kanto, A., & Malo, P. Second, we apply our formulas to parametric density estimation and propose the method of superquantiles (MOS), a simple variation of the method of moments where moments are replaced by superquantiles at different confidence levels. We show that, given a fixed threshold, a single portfolio is the minimal bPOE portfolio for an entire class of distributions simultaneously. First, when portfolio returns are assumed to follow particular distribution families, we show that finding the optimal portfolio via minimization of bPOE has advantages over superquantile minimization. ![]() In particular, we consider two: portfolio optimization and density estimation. Besides providing a useful collection within a single reference, we use these formulas to incorporate the superquantile and bPOE into parametric procedures. In this paper, we derive formulas for the superquantile and bPOE for a variety of common univariate probability distributions. Their use, however, is often made difficult by the lack of well-known closed-form equations for calculating these quantities for commonly used probability distributions. These quantities can prove very useful as the basis for a variety of risk-averse parametric engineering approaches. buffered probability of exceedance (bPOE) is a recently introduced characterization of the tail which is the inverse of CVaR, much like the CDF is the inverse of the quantile. Conditional value-at-risk (CVaR) and value-at-risk, also called the superquantile and quantile, are frequently used to characterize the tails of probability distributions and are popular measures of risk in applications where the distribution represents the magnitude of a potential loss.
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