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The VaR-based Probability Equivalent Level under the Esscher premium principle

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  • Wen, Limin
  • Zhang, Yi

Abstract

This paper investigates the VaR-based Probability Equivalent Level Value (PELV), a risk-adjusted loading coefficient, under the Esscher premium principle. By defining the PELV in terms of the Value at Risk (VaR) at a given confidence level α, we establish a probabilistic coverage condition that incorporates quantile-based risk measures into premium determination. The existence and uniqueness of the PELV are proved under mild moment conditions, and its key properties, including translation invariance, scaling, continuity, and monotonicity with respect to stochastic orders, are systematically examined. Sensitivity analysis demonstrates how the PELV responds to different levels of risk aversion. For practical implementation, we develop a consistent estimator and validate its performance using an empirical case study on Danish fire insurance claims. Numerical results reveal that Esscher premiums rise sharply with increasing confidence levels, emphasizing the importance of tail-sensitive pricing. Overall, this work provides a theoretically sound and practically implementable framework for premium setting under quantile-consistent risk adjustment.

Suggested Citation

  • Wen, Limin & Zhang, Yi, 2025. "The VaR-based Probability Equivalent Level under the Esscher premium principle," Finance Research Letters, Elsevier, vol. 86(PB).
    • Handle: RePEc:eee:finlet:v:86:y:2025:i:pb:s1544612325015387
    DOI: 10.1016/j.frl.2025.108284
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    References listed on IDEAS

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    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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