City Research Online

Differential Sensitivity in Discontinuous Models

Pesenti, S. M., Millossovich, P. ORCID: 0000-0001-8269-7507 & Tsanakas, A. ORCID: 0000-0003-4552-5532 (2023). 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.

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
[thumbnail of Diff_Sensitivity_to_discontinuous_functions.pdf]
Text - Pre-print
Download (1MB) | Preview


Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email


Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login