City Research Online

Abstract

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.

Publication Type:	Monograph (Working Paper)
Additional Information:	Copyright, the authors, 2023.
Publisher Keywords:	Sensitivity analysis, importance measurement, differential sensitivity measures, simulation, risk measures, credit risk
Subjects:	H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management H Social Sciences > HF Commerce
Departments:	Bayes Business School > Actuarial Science & Insurance

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