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Ruin Probabilities as Recurrence Sequences in a Discrete-Time Risk Process

Author

Listed:
  • Ernesto Cruz

    (Facultad de Ciencias, UNAM)

  • Luis Rincón

    (Facultad de Ciencias, UNAM)

  • David J. Santana

    (UJAT, México)

Abstract

The theory of linear recurrence sequences is applied to obtain an explicit formula for the ultimate ruin probability in a discrete-time risk process. It is assumed that the claims distribution is arbitrary but has finite support $$\varvec{\{0,1,\ldots ,m+1\}}$$ { 0 , 1 , … , m + 1 } , for some integer $$\varvec{m\ge 1}$$ m ≥ 1 . The method requires finding the zeroes of an m degree polynomial and solving a system of m linear equations. An approximation is derived and some numerical results and plots are provided as examples.

Suggested Citation

  • Ernesto Cruz & Luis Rincón & David J. Santana, 2024. "Ruin Probabilities as Recurrence Sequences in a Discrete-Time Risk Process," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-16, September.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:3:d:10.1007_s11009-024-10102-0
    DOI: 10.1007/s11009-024-10102-0
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    References listed on IDEAS

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    1. Helena Jasiulewicz & Wojciech Kordecki, 2015. "Ruin probability of a discrete-time risk process with proportional reinsurance and investment for exponential and Pareto distributions," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 25(3), pages 17-38.
    2. Helena Jasiulewicz & Wojciech Kordecki, 2013. "Ruin probability of a discrete-time risk process with proportional reinsurance and investment for exponential and Pareto distributions," Papers 1306.3479, arXiv.org, revised Mar 2015.
    3. Gerber, Hans U., 1988. "Mathematical Fun with the Compound Binomial Process," ASTIN Bulletin, Cambridge University Press, vol. 18(2), pages 161-168, November.
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    5. Sun, L. & Yang, H., 2003. "Ruin Theory in a Discrete Time Risk Model with Interest Income," British Actuarial Journal, Cambridge University Press, vol. 9(3), pages 637-652, August.
    6. Cossette, Hélène & Marceau, Etienne & Maume-Deschamps, Véronique, 2010. "Discrete-Time Risk Models Based on Time Series for Count Random Variables," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 123-150, May.
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