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Indifference pricing of reinsurance with reinstatements using coherent monetary criteria

Abstract

We consider the problem of indifference pricing of reinsurance contracts that contain a reinstatement clause. We define the indifference price relative to both a monetary utility function and a risk measure, to take into account both the risk reduction and the relief of capital immobilization provided by reinsurance. We characterize the indifference price as the unique solution to a fixed point equation and we bound the price by two easily computable values, if one has access to losses simulations. We illustrate our results on a European catastrophe insurance portfolio, and we conduct a simulation study for comparison and reproducibility purposes, where we include the case of dependence between claim arrivals, using Hawkes processes.

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Correspondence to Nabil Kazi-Tani.

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The author gratefully acknowledges the support of the insurer Axa who made its data available, and thanks Thierry Cohignac, Guillaume Gorge and Jean-Sébastien Lagacé for fruitful discussions.

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Kazi-Tani, N. Indifference pricing of reinsurance with reinstatements using coherent monetary criteria. Eur. Actuar. J. 11, 161–183 (2021). https://doi.org/10.1007/s13385-020-00257-8

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Keywords

  • Insurance premium calculation
  • Convex risk measures
  • Monetary utility functions
  • Reinsurance layers
  • Reinstatements

Mathematics Subject Classification

  • 91G05
  • 91B05
  • 91B16
  • 62P05