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Ruin probability in finite time

In: Statistical Tools for Finance and Insurance

Author

Listed:
  • Krzysztof Burnecki

    (Wrocław University of Technology, Hugo Steinhaus Center for Stochastic Methods)

  • Marek Teuerle

    (Wrocław University of Technology, Institute of Mathematics and Computer Science)

Abstract

In examining the nature of the risk associated with a portfolio of business, it is often of interest to assess how the portfolio may be expected to perform over an extended period of time. One approach involves the use of ruin theory (Panjer and Willmot, 1992). Ruin theory is concerned with the excess of the income (with respect to a portfolio of business) over the outgo, or claims paid. This quantity, referred to as insurer’s surplus, varies in time. Specifically, ruin is said to occur if the insurer’s surplus reaches a specified lower bound, e.g. minus the initial capital. One measure of risk is the probability of such an event, clearly reflecting the volatility inherent in the business. In addition, it can serve as a useful tool in long range planning for the use of insurer’s funds.

Suggested Citation

  • Krzysztof Burnecki & Marek Teuerle, 2011. "Ruin probability in finite time," Springer Books, in: Pavel Cizek & Wolfgang Karl Härdle & Rafał Weron (ed.), Statistical Tools for Finance and Insurance, chapter 10, pages 329-348, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18062-0_10
    DOI: 10.1007/978-3-642-18062-0_10
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    Cited by:

    1. is not listed on IDEAS
    2. Krzysztof Burnecki & Rafal Weron, 2006. "Visualization tools for insurance risk processes," HSC Research Reports HSC/06/06, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    3. Pawel Mista, 2006. "Analytical and numerical approach to corporate operational risk modelling," HSC Research Reports HSC/06/03, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    4. 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.
    5. 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.
    6. Yacine Koucha & Alfredo D. Egidio dos Reis, 2021. "Approximations to ultimate ruin probabilities with a Wienner process perturbation," Papers 2107.02537, arXiv.org.
    7. 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.
    8. 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.
    9. 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.
    10. 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.

    More about this item

    Keywords

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    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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