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Ruin probability via Quantum Mechanics Approach

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  • Tamturk, Muhsin
  • Utev, Sergey

Abstract

The finite time ruin probability in the classical surplus process setup with additional capital injections and withdrawals is investigated via the Quantum Mechanics Approach. The results are compared with the Picard–Lefevre Appell Polynomial approach and the traditional Markov Chain approach. In addition, several optimization problems in the insurance market are numerically solved by applying the Quantum Mechanics Approach.

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  • Tamturk, Muhsin & Utev, Sergey, 2018. "Ruin probability via Quantum Mechanics Approach," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 69-74.
    • Handle: RePEc:eee:insuma:v:79:y:2018:i:c:p:69-74
    DOI: 10.1016/j.insmatheco.2017.12.009
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    References listed on IDEAS

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    1. Rulliere, Didier & Loisel, Stephane, 2004. "Another look at the Picard-Lefevre formula for finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 187-203, October.
    2. Dufresne, François & Gerber, Hans U., 1989. "Three Methods to Calculate the Probability of Ruin," ASTIN Bulletin, Cambridge University Press, vol. 19(1), pages 71-90, April.
    3. Zhou, Ming & Yuen, Kam C., 2012. "Optimal reinsurance and dividend for a diffusion model with capital injection: Variance premium principle," Economic Modelling, Elsevier, vol. 29(2), pages 198-207.
    4. Cai, Jun & Dickson, David C.M., 2004. "Ruin probabilities with a Markov chain interest model," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 513-525, December.
    5. Cardoso, Rui M. R. & Egidio dos Reis, Alfredo D., 2002. "Recursive calculation of time to ruin distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 219-230, April.
    6. Nie, Ciyu & Dickson, David C. M. & Li, Shuanming, 2011. "Minimizing the ruin probability through capital injections," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 195-209, September.
    7. Ignatov, Zvetan G. & Kaishev, Vladimir K. & Krachunov, Rossen S., 2001. "An improved finite-time ruin probability formula and its Mathematica implementation," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 375-386, December.
    8. Asmussen, S. & Binswanger, K., 1997. "Simulation of Ruin Probabilities for Subexponential Claims," ASTIN Bulletin, Cambridge University Press, vol. 27(2), pages 297-318, November.
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    Cited by:

    1. 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.
    2. Jorge Wilson Euphasio Junior & João Vinícius França Carvalho, 2022. "Resseguro e Capital de Solvência: Atenuantes da Probabilidade de Ruína de SeguradorasReinsurance and Solvency Capital: Mitigating Insurance Companies’ Ruin Probability," RAC - Revista de Administração Contemporânea (Journal of Contemporary Administration), ANPAD - Associação Nacional de Pós-Graduação e Pesquisa em Administração, vol. 26(1), pages 200191-2001.
    3. Emilio Gómez-Déniz & José María Sarabia & Enrique Calderín-Ojeda, 2019. "Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem," Risks, MDPI, vol. 7(2), pages 1-16, June.
    4. Claude Lefèvre & Stéphane Loisel & Muhsin Tamturk & Sergey Utev, 2018. "A Quantum-Type Approach to Non-Life Insurance Risk Modelling," Risks, MDPI, vol. 6(3), pages 1-17, September.
    5. 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.
    6. Muhsin Tamturk, 2023. "Quantum Computing in Insurance Capital Modelling," Mathematics, MDPI, vol. 11(3), pages 1-13, January.

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