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Sensitivity Analysis Using Risk Measures.

Andreas Tsanakas1, Pietro Millossovich1

  • 1Faculty of Actuarial Science and Insurance, Cass Business School, City University, London, UK.

Risk Analysis : an Official Publication of the Society for Risk Analysis
|November 11, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a novel sensitivity analysis method for quantitative models with uncertain inputs. It links output risk measure derivatives to input uncertainty, providing a global sensitivity measure for better risk assessment.

Keywords:
Aggregationdependenceparameter uncertaintyrisk measuressensitivity analysisuncertainty analysis

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Area of Science:

  • Quantitative Finance
  • Risk Management
  • Statistical Modeling

Background:

  • Uncertainty in quantitative models necessitates robust risk measures.
  • Sensitivity analysis is crucial for understanding model behavior and input influence.
  • Existing methods may not fully integrate sensitivity and uncertainty analyses.

Purpose of the Study:

  • To develop a global sensitivity measure by analyzing the derivatives of output risk measures with respect to model inputs.
  • To explicitly link sensitivity analysis and uncertainty quantification.
  • To provide a method applicable to distortion risk measures and extendable to various parameter types.

Main Methods:

  • Proposing a sensitivity analysis method based on derivatives of output risk measures.
  • Deriving a representation for the sensitivity measure evaluable on Monte Carlo samples.
  • Employing nonparametric techniques for gradient estimation when analytical models are intractable.
  • Extending the framework to assess sensitivity to constant, statistical, and random parameters.

Main Results:

  • A novel global sensitivity measure is introduced, directly connecting input uncertainty to output risk.
  • The method allows for evaluation using Monte Carlo simulations via weighted averages of gradients.
  • Demonstrated applicability on a nonlinear insurance loss model.
  • Successfully extended to measure sensitivity to different types of model parameters and dependencies.

Conclusions:

  • The proposed sensitivity analysis method effectively quantifies the impact of input uncertainty on output risk measures.
  • This approach offers a unified framework for sensitivity and uncertainty analysis in quantitative modeling.
  • The method is versatile, applicable to various risk measures and model complexities, including insurance loss modeling.