Robustness and sensitivity of risk evaluations

This thesis is a collection of three contributions to sensitivity analysis of financial and insurance risk evaluations. Sensitivity analysis constitutes an important component of model building, interpretation and validation, particularly for models whose output is at the core of a risk management decision process. We study models comprising a (random) vector of input factors, an aggregation function mapping input factors to a random output, and a risk measure applied to the output. In most typical insurance and financial applications, the model’s characteristic – a non-analytical and numerically expensive aggregation function evaluated on numerous input factors – renders most sensitivity analysis methodologies unfeasible. We develop sensitivity analysis procedures applicable specifically for the above model setting. First, we address the estimation of risk measures applied to the model output. The fundamental purpose of a risk measure is to distinguish between different risk profiles. However, strong assumptions on the risk measure’s ability to distinguish risk severities lead to non robust estimators. We provide conditions when risk measures exhibit both, robustness and a consistent ranking of risks. Second, we develop a framework termed reverse sensitivity testing, that associates a critical increase in the risk measure to specific input factors. We provide analytical solutions of the stressed distribution of input factors that lead to the required increase in the outputs’ risk measure. Third, we introduce a novel sensitivity measure, which quantifies the extent to which the model output is affected by a stress in an individual input factor. Compared to other sensitivity measures in the literature, the proposed measure incorporates the direct impact of the stressed input as well as indirect effects via other input factors that are dependent on the one being stressed. In this way the dependence between inputs is explicitly taken into account

Reverse sensitivity testing: What does it take to break the model?

Sensitivity analysis is an important component of model building, interpretation and validation. A model comprises a vector of random input factors, an aggregation function mapping input factors to a random output, and a (baseline) probability measure. A risk measure, such as Value-at-Risk and Expected Shortfall, maps the distribution of the output to the real line. As is common in risk management, the value of the risk measure applied to the output is a decision variable. Therefore, it is of interest to associate a critical increase in the risk measure to specific input factors. We propose a global and model-independent framework, termed ‘reverse sensitivity testing’, comprising three steps: (a) an output stress is specified, corresponding to an increase in the risk measure(s); (b) a (stressed) probability measure is derived, minimising the Kullback-Leibler divergence with respect to the baseline probability, under constraints generated by the output stress; (c) changes in the distributions of input factors are evaluated. We argue that a substantial change in the distribution of an input factor corresponds to high sensitivity to that input and introduce a novel sensitivity measure to formalise this insight. Implementation of reverse sensitivity testing in a Monte-Carlo setting can be performed on a single set of input/output scenarios, simulated under the baseline model. Thus the approach circumvents the need for additional computationally expensive evaluations of the aggregation function. We illustrate the proposed approach through a numerical example of a simple insurance portfolio and a model of a London Insurance Market portfolio used in industry

Euler allocations in the presence of non-linear reinsurance: comment on Major (2018)

Major (2018) discusses Euler/Aumann-Shapley allocations for non-linear portfolios. He argues convincingly that many (re)insurance portfolios, while non-linear, are nevertheless positively homogeneous, owing to the way that deductibles and limits are typically set. For such non-linear but homogeneous portfolio structures, he proceeds with defining and studying a particular type of capital allocation. In this comment, we build on Major's (2018) insights but take a slightly different direction, to consider Euler capital allocations for distortion risk measures applied to homogeneous portfolios. Thus, the important problem of capital allocation in portfolios with non-linear reinsurance is solved

Relationship between molecular connectivity and carcinogenic activity: a confirmation with a new software program based on graph theory.

For a database of 826 chemicals tested for carcinogenicity, we fragmented the structural formula of the chemicals into all possible contiguous-atom fragments with size between two and eight (nonhydrogen) atoms. The fragmentation was obtained using a new software program based on graph theory. We used 80% of the chemicals as a training set and 20% as a test set. The two sets were obtained by random sorting. From the training sets, an average (8 computer runs with independently sorted chemicals) of 315 different fragments were significantly (p < 0.125) associated with carcinogenicity or lack thereof. Even using this relatively low level of statistical significance, 23% of the molecules of the test sets lacked significant fragments. For 77% of the molecules of the test sets, we used the presence of significant fragments to predict carcinogenicity. The average level of accuracy of the predictions in the test sets was 67.5%. Chemicals containing only positive fragments were predicted with an accuracy of 78.7%. The level of accuracy was around 60% for chemicals characterized by contradictory fragments or only negative fragments. In a parallel manner, we performed eight paired runs in which carcinogenicity was attributed randomly to the molecules of the training sets. The fragments generated by these pseudo-training sets were devoid of any predictivity in the corresponding test sets. Using an independent software program, we confirmed (for the complex biological endpoint of carcinogenicity) the validity of a structure-activity relationship approach of the type proposed by Klopman and Rosenkranz with their CASE program

Effect of cyclic loading on hydrogen diffusion in low carbon steels

Carbon steels or low-alloyed steels may be affected by damaging phenomena due to Hydrogen Embrittlement (HE), which is a particular form of Environmental Assisted Cracking (EAC). The insurgence of HE depends on the intrinsic susceptibility of the steel, the applied stress, and the concentration of hydrogen inside the metal. It occurs by a mechanism of absorption and subsequent diffusion of atomic hydrogen through the metal lattice. On steels with a yield strength lower than 700 MPa, HE occurs in the plastic deformation field, in the presence of dynamic loading at slow strain rates or cyclic fatigue loading at very low frequencies. Although several important studies were carried out on the effect of loading conditions on hydrogen diffusion into the metal and HE mechanism, HE phenomena are not fully understood. In this work, the effect of the application of cyclic loads on hydrogen diffusion parameters was studied both in the elastic and in the plastic deformation field. The influence of mean load and amplitude was analyzed. Hydrogen permeation tests were performed on API 5L X65 steel, in accordance with ISO 17081:2014. The specimen behaved as bi-electrode between the two compartments of a Devanathan-Stachurski cell. The anodic side of the specimen was polarized at +340 mV vs Ag/AgCl in a 0.1 M NaOH aerated solution, while the cathodic compartment was filled with an aerated borate solution. A controller enabled temperature adjustment at 20±0.5°C. Once the passivity current registered in the anodic side reached values of 0.05 µA/cm2, a cathodic current density of 0.50 mA/cm2 was applied to charging cathodic side. The study included tests with sine waveform cycling loading, with a maximum level equal to 110% TYS, at a frequency of 10-2 Hz. The results confirmed the values of hydrogen diffusion coefficient usually indicated for low-alloyed steels with a sorbitic microstructure. Strain hardened specimens - stretched above yield strength - showed an increase of steady state current and an extension of the time lag, denoting a slight decrease in the apparent hydrogen diffusion coefficient due to traps effect in the cold deformed steel matrix. Under cyclic loading, an instantaneous peak of current with a subsequent significant transient decrease occurred after cyclic load application, whereas no relevant variation of permeation curve compared to unloaded specimens was observed if specimens were already loaded before hydrogen charging. The instantaneous current peak reached values much higher than the steady state current. This is ascribed to the rupture of the passive film – caused by loading – and its subsequent reformation; in fact, this can also be noted during tests performed on specimens without hydrogen permeation. The following transient, in which the permeation current decreases below the steady state and then returns to it, denotes a relevant trapping effect that causes the instantaneous reduction of mobile hydrogen concentration in the lattice. This becomes more significant for loads closer and closer to the yield strength, mainly beyond this, and can only be noted at the first loading step. Subsequent unloading and loading step at the same mean value showed no transient in the permeation curren

Analysis of BRCA1 and RAD51C promoter methylation in italian families at high-risk of breast and ovarian cancer

Previous studies on breast and ovarian carcinoma (BC and OC) revealed constitutional BRCA1 and RAD51C promoter hypermethylation as epigenetic alterations leading to tumor predisposition. Nevertheless, the impact of epimutations at these genes is still debated. One hundred and eight women affected by BC, OC, or both and considered at very high risk of carrying BRCA1 germline mutations were studied. All samples were negative for pathogenic variants or variants of uncertain significance at BRCA testing. Quantitative BRCA1 and RAD51C promoter methylation analyses were performed by Epityper mass spectrometry on peripheral blood samples and results were compared with those in controls. All the 108 analyzed cases showed methylation levels at the BRCA1/RAD51C promoter comparable with controls. Mean methylation levels (\ub1 stdev) at the BRCA1 promoter were 4.3% (\ub1 1.4%) and 4.4% (\ub1 1.4%) in controls and patients, respectively (p &gt; 0.05; t-test); mean methylation levels (\ub1 stdev) at the RAD51C promoter were 4.3% (\ub1 0.9%) and 3.7% (\ub1 0.9%) in controls and patients, respectively (p &gt; 0.05; t-test). Based on these observations; the analysis of constitutional methylation at promoters of these genes does not seem to substantially improve the definition of cancer risks in patients. These data support the idea that epimutations represent a very rare event in high-risk BC/OC populations

A highly-collimated SiO jet in the HH212 protostellar outflow

We mapped the HH212 Class 0 outflow in SiO(2--1, 5--4) and continuum using the PdBI in its extended configurations. The unprecedented angular resolution (down to 0.34") allows accurate comparison with a new, deep H2 image obtained at the VLT. The SiO emission is confined to a highly-collimated bipolar jet (width 0.35") along the outflow axis. The jet can be traced down to within 500 AU of the protostar, in a region that is heavily obscured in H2 images. Where both species are detected, SiO shows the same overall kinematics and structure as H2, indicating that both molecules are tracing the same material. We find that the high-velocity SiO gas near the protostar is not tracing a wide-angle wind but is already confined to a flow inside a narrow cone of half-opening angle < 6 deg.Comment: Astronomy and Astrophysics Letter, in pres