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Discrete-time Insurance Model with Capital Injections and Reinsurance

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Abstract

A periodic-review insurance model is considered under the following assumptions. In order to avoid ruin the insurer maintains the company surplus above a chosen level a by capital injections at the end of each period. One-period insurance claims form a sequence of independent identically distributed nonnegative random variables with finite mean. A nonproportional reinsurance is applied for minimization of total expected discounted injections during a given planning horizon of n periods. Insurance and reinsurance premiums are calculated using the expected value principle. Optimal reinsurance strategy is established. Numerical results illustrating the theoretical ones are provided for three claims distributions.

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, Lomonosov Moscow State University, Moscow, 119991, Russia

    Ekaterina Bulinskaya, Julia Gusak & Anastasia Muromskaya

Authors
  1. Ekaterina Bulinskaya
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  2. Julia Gusak
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  3. Anastasia Muromskaya
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Corresponding author

Correspondence to Ekaterina Bulinskaya.

Additional information

The research is supported by Russian Foundation for Basic Research, grant 13-01-00653.

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Bulinskaya, E., Gusak, J. & Muromskaya, A. Discrete-time Insurance Model with Capital Injections and Reinsurance. Methodol Comput Appl Probab 17, 899–914 (2015). https://doi.org/10.1007/s11009-014-9418-3

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  • DOI: https://doi.org/10.1007/s11009-014-9418-3

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