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Approximate Formula for Adjustment Coefficient of a Non-linear Risk Model with Weibull Claims

In: Quantitative Methods and Data Analysis in Applied Demography - Volume 2

Author

Listed:
  • Basak Gever

    (University of Turkish Aeronautical and Association, Department of Industrial Engineering)

  • Tahir Khaniyev

    (TOBB University of Economics and Technology, Department of Industrial Engineering
    The Center of Digital Economics, Azerbaijan State University of Economics)

Abstract

This study examines a non-linear Cramér-Lundberg risk model, in order to determine the adjustment coefficient (r) when the claims have Weibull distribution. Similar insurance models have been studied in the literature, usually when premiums are linear. However, in some real-world problems, the increase in revenue may not be linear. In such cases, it is significant to consider nonlinear risk models. Accordingly, in this study, a nonlinear Cramér-Lundberg risk model is mathematically constructed and investigated when the premium function is p ( t ) = c t $$ p(t)=c\sqrt{t} $$ . As is known, the adjustment coefficient plays a substantial role in evaluating the ruin probability. Thus, a detailed examination of this coefficient is important. However, it is a challenging process to derive the exact value of r from an integral equation when the claims have Weibull distribution. For this reason, the adjustment coefficient is investigated in this study by using approximation methods and a practical algorithm proposed to calculate approximate result with the desired closeness to the true value.

Suggested Citation

  • Basak Gever & Tahir Khaniyev, 2025. "Approximate Formula for Adjustment Coefficient of a Non-linear Risk Model with Weibull Claims," The Springer Series on Demographic Methods and Population Analysis, in: Christos H. Skiadas & Charilaos Skiadas (ed.), Quantitative Methods and Data Analysis in Applied Demography - Volume 2, chapter 0, pages 211-224, Springer.
    • Handle: RePEc:spr:ssdmcp:978-3-031-82279-7_17
    DOI: 10.1007/978-3-031-82279-7_17
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