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Optimal Reinsurance via Dirac-Feynman Approach

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  • Muhsin Tamturk

    (University of Leicester)

  • Sergey Utev

    (University of Leicester)

Abstract

In this paper, the Dirac-Feynman path calculation approach is applied to analyse finite time ruin probability of a surplus process exposed to reinsurance by capital injections. Several reinsurance optimization problems on optimum insurance and reinsurance premium with respect to retention level are investigated and numerically illustrated. The retention level is chosen to decrease the finite time ruin probability and to guarantee that reinsurance premium covers an average of overall capital injections. All computations are based on Dirac-Feynman path calculation approach applied to the convolution type operators perturbed by Injection operator (shift type operator). In addition, the effect of the Injection operator on ruin probability is analysed.

Suggested Citation

  • Muhsin Tamturk & Sergey Utev, 2019. "Optimal Reinsurance via Dirac-Feynman Approach," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 647-659, June.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:2:d:10.1007_s11009-018-9674-8
    DOI: 10.1007/s11009-018-9674-8
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    References listed on IDEAS

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    4. Castañer, A. & Claramunt, M.M. & Lefèvre, C., 2013. "Survival probabilities in bivariate risk models, with application to reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 632-642.
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    Cited by:

    1. Muhsin Tamturk, 2023. "Quantum Computing in Insurance Capital Modelling," Mathematics, MDPI, vol. 11(3), pages 1-13, January.
    2. Muhsin Tamturk & Dominic Cortis & Mark Farrell, 2020. "Examining the Effects of Gradual Catastrophes on Capital Modelling and the Solvency of Insurers: The Case of COVID-19," Risks, MDPI, vol. 8(4), pages 1-13, December.

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