Robust distortion risk measures with linear penalty under distribution uncertainty

Key Points

• The robust distortion risk measure is influenced by linear penalty functions applied under distribution uncertainty, enhancing decision-making in uncertain environments.
• The study establishes an explicit characterization of optimal quantile distributions and associated value functions, deepening understanding in risk assessment.
• By extending results from previous research, the paper enriches the framework of robust distortion risk measures and their applications in finance.
• Findings reveal how variations in penalty parameters impact the solutions, providing insights for effective risk management strategies.