Indifference Pricing of Reinsurance with Reinstatements Using Coherent Monetary Criteria

Nabil Kazi-Tani ()
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Nabil Kazi-Tani: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon

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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.

Keywords: Insurance premium calculation; Convex risk measures; Concave monetary utility functions; Reinstatements; Reinsurance layers (search for similar items in EconPapers)
Date: 2021-01-18
Note: View the original document on HAL open archive server: https://hal.science/hal-01742638v2
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Published in European Actuarial Journal, 2021, 11 (1), pp.161-183. ⟨10.1007/s13385-020-00257-8⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01742638

DOI: 10.1007/s13385-020-00257-8

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