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Risk aggregation considering probabilistic and consequential interactions: A general formulation with computational

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Summary
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This study introduces a novel risk aggregation method that accounts for complex interactions between risk events. This approach enhances accuracy in risk management, particularly in subjective assessments.

Keywords:
approximate risk measureconsequential interactionprobabilistic interactionrisk aggregation

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Area of Science:

  • Risk Management
  • Decision Analysis
  • Quantitative Finance

Background:

  • Accurate risk aggregation is crucial for effective risk management.
  • Existing methods struggle with complex interactions between risk events, limiting universal application.
  • Subjective risk assessment contexts present unique challenges for current aggregation techniques.

Purpose of the Study:

  • To propose a theoretically sound risk aggregation method incorporating diverse interaction types.
  • To enhance the universality and effectiveness of risk aggregation for decision analysis.
  • To address limitations in current approaches, especially within subjective risk assessment.

Main Methods:

  • Developing rigorous definitions, measures, and graphical representations for various interaction types.
  • Formulating a generalized risk aggregation approach applicable to both objective and subjective contexts.
  • Analyzing the additivity of risks and risk sets, clarifying conditions for additivity.
  • Introducing quasi-two/three-additive measures to reduce computational costs while maintaining reliability.

Main Results:

  • The proposed method provides a comprehensive framework for risk aggregation with interaction.
  • Enhanced accuracy and applicability across objective and subjective risk assessment scenarios.
  • Clarified conditions for risk additivity and introduced computationally efficient approximation methods.
  • Demonstrated practical utility through a detailed case study.

Conclusions:

  • The developed risk aggregation method effectively integrates complex interactions, improving accuracy.
  • The approach offers a universal solution applicable to diverse risk assessment contexts.
  • Quasi-additive measures provide a practical means to reduce computational burden without sacrificing reliability.