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

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

Risk margin for a non-life insurance run-off

For solvency purposes insurance companies need to calculate so-called best-estimate reserves for outstanding loss liability cash flows and a corresponding risk margin for non-hedgeable insurance-technical risks in these cash flows. In actuarial practice, the calculation of the risk margin is often not based on a sound model but various simplified methods are used. In the present paper we properly define these notions and we introduce insurance-technical probability distortions. We describe how the latter can be used to calculate a risk margin for non-life insurance run-off liabilities in a mathematically consistent way

A theory of multivariate stress testing

We present a theoretical framework for stressing multivariate stochastic models. We consider a stress to be a change of measure, placing a higher weight on multivariate scenarios of interest. In particular, a stressing mechanism is a mapping from random vectors to RadonNikodym densities. We postulate desirable properties for stressing mechanisms addressing alternative objectives. Consistently with our focus on dependence, we require throughout invariance to monotonic transformations of risk factors. We study in detail the properties of two families of stressing mechanisms, based respectively on mixtures of univariate stresses and on transformations of statistics we call Spearman and Kendall’s cores. Furthermore, we characterize the aggregation properties of those stressing mechanisms, which motivate their use in deriving new capital allocation methods, with properties different to those typically found in the literature. The proposed methods are applied to stress testing and capital allocation, using the simulation model of a UK-based non-life insurer

Differential Sensitivity in Discontinuous Models

Differential sensitivity measures provide valuable tools for interpreting complex computational models used in applications ranging from simulation to algorithmic prediction. Taking the derivative of the model output in direction of a model parameter can reveal input-output relations and the relative importance of model parameters and input variables. Nonetheless, it is unclear how such derivatives should be taken when the model function has discontinuities and/or input variables are discrete. We present a general framework for addressing such problems, considering derivatives of quantile-based output risk measures, with respect to distortions to random input variables (risk factors), which impact the model output through step-functions. We prove that, subject to weak technical conditions, the derivatives are well-defined and derive the corresponding formulas. We apply our results to the sensitivity analysis of compound risk models and to a numerical study of reinsurance credit risk in a multi-line insurance portfolio

Scenario Weights for Importance Measurement (SWIM) – an R package for sensitivity analysis

The SWIM package implements a flexible sensitivity analysis framework, based primarily on results and tools developed by Pesenti et al. (2019). SWIM provides a stressed version of a stochastic model, subject to model components (random variables) fulfilling given probabilistic constraints (stresses). Possible stresses can be applied on moments, probabilities of given events, and risk measures such as Value-at-Risk and Expected Shortfall. SWIM operates upon a single set of simulated scenarios from a stochastic model, returning scenario weights, which encode the required stress and allow monitoring the impact of the stress on all model components. The scenario weights are calculated to minimise the relative entropy with respect to the baseline model, subject to the stress applied. As well as calculating scenario weights, the package provides tools for the analysis of stressed models, including plotting facilities and evaluation of sensitivity measures. SWIM does not require additional evaluations of the simulation model or explicit knowledge of its underlying statistical and functional relations; hence it is suitable for the analysis of black box models. The capabilities of SWIM are demonstrated through a case study of a credit portfolio model

DIANA-microT web server: elucidating microRNA functions through target prediction

Computational microRNA (miRNA) target prediction is one of the key means for deciphering the role of miRNAs in development and disease. Here, we present the DIANA-microT web server as the user interface to the DIANA-microT 3.0 miRNA target prediction algorithm. The web server provides extensive information for predicted miRNA:target gene interactions with a user-friendly interface, providing extensive connectivity to online biological resources. Target gene and miRNA functions may be elucidated through automated bibliographic searches and functional information is accessible through Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways. The web server offers links to nomenclature, sequence and protein databases, and users are facilitated by being able to search for targeted genes using different nomenclatures or functional features, such as the genes possible involvement in biological pathways. The target prediction algorithm supports parameters calculated individually for each miRNA:target gene interaction and provides a signal-to-noise ratio and a precision score that helps in the evaluation of the significance of the predicted results. Using a set of miRNA targets recently identified through the pSILAC method, the performance of several computational target prediction programs was assessed. DIANA-microT 3.0 achieved there with 66% the highest ratio of correctly predicted targets over all predicted targets. The DIANA-microT web server is freely available at www.microrna.gr/microT

The European DISABKIDS project: development of seven condition-specific modules to measure health related quality of life in children and adolescents

BACKGROUND: The European DISABKIDS project aims to enhance the Health Related Quality of Life (HRQoL) of children and adolescents with chronic medical conditions and their families. We describe the development of the seven cross-nationally tested condition-specific modules of the European DISABKIDS HRQoL instrument in a population of children and adolescents. The condition-specific modules are intended for use in conjunction with the DISABKIDS chronic generic module. METHODS: Focus groups were used to construct the pilot version of the DISABKIDS condition-specific HRQoL modules for asthma, juvenile idiopathic arthritis, atopic dermatitis, cerebral palsy, cystic fibrosis, diabetes and epilepsy. Analyses were conducted on pilot test data in order to construct field test versions of the modules. A series of factor analyses were run, first, to determine potential structures for each condition-specific module, and, secondly, to select a reduced number of items from the pilot test to be included in the field test. Post-field test analyses were conducted to retest the domain structure for the final DISABKIDS condition-specific modules. RESULTS: The DISABKIDS condition-specific modules were tested in a pilot study of 360 respondents, and subsequently in a field test of 1152 respondents in 7 European countries. The final condition-specific modules consist of an 'Impact' domain and an additional domain (e.g. worry, stigma, treatment) with between 10 to 12 items in total. The Cronbach's alpha of the final domains was found to vary from 0.71 to 0.90. CONCLUSION: The condition-specific modules of the DISABKIDS instrument were developed through a step-by-step process including cognitive interview, clinical expertise, factor analysis, correlations and internal consistency. A cross-national pilot and field test were necessary to collect these data. In general, the internal consistency of the domains was satisfactory to high. In future, the DISABKIDS instrument may serve as a useful tool with which to assess HRQoL in children and adolescents with a chronic condition. The condition-specific modules can be used in conjunction with the DISABKIDS chronic generic module