Optimal portfolios in the presence of stress scenarios A worst-case approach

Insurance companies and banks regularly have to face stress tests performed by regulatory instances. To model their investment decision problems that includes stress scenarios, we propose the worst-case portfolio approach. Thus, the resulting optimal portfolios are already stress test prone by construction. A central issue of the worst-case portfolio approach is that neither the time nor the order of occurrence of the stress scenarios are known. Even more, there are no probabilistic assumptions regarding the occurrence of the stresses. By defining the relative worst-case loss and introducing the concept of minimum constant portfolio processes, we generalize the traditional concepts of the indifference frontier and the indifference-optimality principle. We prove the existence of a minimum constant portfolio process that is optimal for the multi-stress worst-case problem. As a main result we derive a verification theorem that provides conditions on Lagrange multipliers and nonlinear ordinary differential equations that support the construction of optimal worst-case portfolio strategies. The practical applicability of the verification theorem is demonstrated via numerical solution of various worst-case problems with stresses. There, it is in particular shown that an investor who chooses the worst-case optimal portfolio process may have a preference regarding the order of stresses, but there may also be stress scenarios where he/she is indifferent regarding the order and time of occurrence.

Model risk in mean-variance portfolio selection: an analytic solution to the worst-case approach

In this paper we consider the worst-case model risk approach described in Glasserman and Xu (Quant Finance 14(1):29–58, 2014). Portfolio selection with model risk can be a challenging operational research problem. In particular, it presents an additional optimisation compared to the classical one. We find the analytical solution for the optimal mean-variance portfolio selection in the worst-case scenario approach and for the special case with the additional constraint of a constant mean vector considered in Glasserman and Xu (Quant Finance 14(1):29–58, 2014). Moreover, we prove in two relevant cases—the minimum-variance case and the symmetric case, i.e. when all assets have the same mean—that the analytical solutions in the alternative model and in the nominal one are equal; we show that this corresponds to the situation when model risk reduces to estimation risk.

Mercury Methylation Upon Coastal Sediment Resuspension: A Worst-case Approach Under Dark Conditions

Mercury behavior upon resuspension of sediments from two impacted areas of Guanabara Bay was evaluated to assess worst-case methylmercury (MeHg) responses, under dark experimental conditions. Total mercury (THg) and MeHg concentrations were determined along 24 hours experiments of sediment resuspension in the bay water. Fine-grained Meriti River estuary (MR) sediments had 8-times higher MeHg initial concentrations than sandy Rio the Janeiro Harbor (RJH) sediments (3.4 ± 0.29 vs. 0.41 ± 0.1 ng g− 1, respectively).THg contents were uncorrelated with resuspension time, while correlations of resuspension time with MeHg (r2 = 0.66) and %MeHg in relation to THg (r2 = 0.75) were observed only for RJH sediments. These findings correspond to a 2.8-times MeHg concentration increase (ΔMeHg = 0.75 ng g− 1) and 4.4-times increase in %MeHg (Δ%MeHg = 1.0%) for station RJH.This suggests that assessments of MeHg spatial-temporal variability can be limited if concentration changes due to sediment resuspension are not considered.

Analysis of the specificity of the SD Biosensor Standard Q Ag-Test based on Slovak mass testing data

From 31.10. - 1.11.2020 Slovakia has used the SD Biosensor Standard Q Ag-Test for nationwide tests for SARS-CoV-2, in which 3,625,332 persons from 79 counties were tested. Based on this data, we calculate that the specificity of the test is at least 99.6% (with a 97.5% one-sided lower confidence bound). Our analysis is based on a worst case approach in which all positives are assumed to be false positives. Therefore, the actual specificity is expected to exceed 99.6%.

Minimum description length revisited

This is an up-to-date introduction to and overview of the Minimum Description Length (MDL) Principle, a theory of inductive inference that can be applied to general problems in statistics, machine learning and pattern recognition. While MDL was originally based on data compression ideas, this introduction can be read without any knowledge thereof. It takes into account all major developments since 2007, the last time an extensive overview was written. These include new methods for model selection and averaging and hypothesis testing, as well as the first completely general definition of MDL estimators. Incorporating these developments, MDL can be seen as a powerful extension of both penalized likelihood and Bayesian approaches, in which penalization functions and prior distributions are replaced by more general luckiness functions, average-case methodology is replaced by a more robust worst-case approach, and in which methods classically viewed as highly distinct, such as AIC versus BIC and cross-validation versus Bayes can, to a large extent, be viewed from a unified perspective.

Automation of fuzzy multi-criteria selection of robotic machine-assembly technologies using worst-case approach

In this paper a new method of selection of robotic machine-assembly technology is presented. The core of the technology suggested is the method of fuzzy multi-criteria alternatives selection using the worst-case approach. The automation of the proposed solution is based on the original WMS (Worst Method Solution) software, developed by authors. In the basis of this software are the ideas of robotic machine-assembly technology and its theoretical formalization.