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Ruin Probability in Finite Time

Author

Listed:
  • Krzysztof Burnecki
  • Marek Teuerle

Abstract

The ruin probability in finite time can only be calculated analytically for a few special cases of the claim amount distribution. The most classic example is discussed in Section 1.2. The value can always be computed directly using Monte Carlo simulations, however, this is usually a time-consuming procedure. Thus, finding a reliable approximation is really important from a practical point of view. The most important approximations of the finite time ruin probability are presented in Section 1.3. They are further illustrated in Section 1.4 using the Danish fire losses dataset, which concerns major fire losses in profits that occurred between 1980 and 2002 and were recorded by Copenhagen Re.

Suggested Citation

  • Krzysztof Burnecki & Marek Teuerle, 2010. "Ruin Probability in Finite Time," HSC Research Reports HSC/10/04, Hugo Steinhaus Center, Wroclaw University of Technology.
    • Handle: RePEc:wuu:wpaper:hsc1004
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    File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_10_04.pdf
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    References listed on IDEAS

    as
    1. Dickson,David C. M., 2010. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521176750.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Krzysztof Burnecki & Rafal Weron, 2006. "Visualization tools for insurance risk processes," HSC Research Reports HSC/06/06, Hugo Steinhaus Center, Wroclaw University of Technology.
    2. Pawel Mista, 2006. "Analytical and numerical approach to corporate operational risk modelling," HSC Research Reports HSC/06/03, Hugo Steinhaus Center, Wroclaw University of Technology.
    3. Krzysztof Burnecki & Marek A. Teuerle & Aleksandra Wilkowska, 2021. "Ruin Probability for the Insurer–Reinsurer Model for Exponential Claims: A Probabilistic Approach," Risks, MDPI, vol. 9(5), pages 1-10, May.
    4. Başak Bulut Karageyik & Şule Şahin, 2017. "Determination of the Optimal Retention Level Based on Different Measures," JRFM, MDPI, vol. 10(1), pages 1-21, January.
    5. Yacine Koucha & Alfredo D. Egidio dos Reis, 2021. "Approximations to ultimate ruin probabilities with a Wienner process perturbation," Papers 2107.02537, arXiv.org.
    6. Agata Boratyńska & Krzysztof Kondraszuk, 2013. "Odporność składki kwantylowej na ε-zaburzenie rozkładu liczby szkód," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 117-136.
    7. David J. Santana & Juan González-Hernández & Luis Rincón, 2017. "Approximation of the Ultimate Ruin Probability in the Classical Risk Model Using Erlang Mixtures," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 775-798, September.
    8. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
    9. Franck Adékambi & Kokou Essiomle, 2020. "Ruin Probability for Stochastic Flows of Financial Contract under Phase-Type Distribution," Risks, MDPI, vol. 8(2), pages 1-21, May.

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    More about this item

    Keywords

    Insurance risk model; Ruin probability; Segerdahl approximation; De Vylder approximation; Diffusion approximation; Brownian motion; Levy motion;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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