Optimal Premium allocation understop-loss insurance using exposure curves

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Mert Ö. M., Kestel A. S.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.1, no.1, pp.1-20, 2022 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 1 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.15672/hjms.xx
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1-20
  • Middle East Technical University Affiliated: Yes

Abstract

Determining the retention level in the stop-loss insurance risk premium for both insurer

and reinsurer is an important factor in pricing. This paper aims to set optimal reinsurance

with respect to the joint behavior of the insurer and the reinsurer under stop-loss contracts.

The dependence between the costs of insurer and reinsurer is expressed as a function of

retention (d) and maximum-cap (m) levels. Based on the maximum degree of correlation,

the optimal levels for d and m are derived under certain claim distributions (Pareto,

Gamma and Inverse Gamma). Accordingly, the risk premium and exposure curves for

both parties are based on the selected distributions. Quantification of the premium share

over derived exposure curves based on the optimized retention and maximum levels and

the maximum loss risk is obtained using VaR and CVaR as risk measures.