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Minimising expected discounted capital injections by reinsurance in a classical risk model

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  • Julia Eisenberg
  • Hanspeter Schmidli

Abstract

In this paper we consider a classical continuous time risk model, where the claims are reinsured by some reinsurance with retention level , where means ‘no reinsurance’ and b=0 means ‘full reinsurance’. The insurer can change the retention level continuously. To prevent negative surplus the insurer has to inject additional capital. The problem is to minimise the expected discounted cost over all admissible reinsurance strategies. We show that an optimal reinsurance strategy exists. For some special cases we will be able to give the optimal strategy explicitly. In other cases the method will be illustrated only numerically.

Suggested Citation

  • Julia Eisenberg & Hanspeter Schmidli, 2011. "Minimising expected discounted capital injections by reinsurance in a classical risk model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2011(3), pages 155-176.
    • Handle: RePEc:taf:sactxx:v:2011:y:2011:i:3:p:155-176
    DOI: 10.1080/03461231003690747
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    Cited by:

    1. Federico, Salvatore & Ferrari, Giorgio & Torrente, Maria Laura, 2023. "Irreversible Reinsurance: Minimization of Capital Injections in Presence of a Fixed Cost," Center for Mathematical Economics Working Papers 682, Center for Mathematical Economics, Bielefeld University.
    2. Teng, Ye & Zhang, Zhimin, 2023. "On a time-changed Lévy risk model with capital injections and periodic observation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 290-314.
    3. Goreac, Dan & Li, Juan & Wang, Pangbo & Xu, Boxiang, 2024. "Linearisation techniques and the dual algorithm for a class of mixed singular/continuous control problems in reinsurance. Part II: Numerical aspects," Applied Mathematics and Computation, Elsevier, vol. 473(C).

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