IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v424y2022ics0096300322000558.html
   My bibliography  Save this article

Compound binomial risk model in a Markovian environment with capital cost and the calculation algorithm

Author

Listed:
  • XIAO, Lin

Abstract

The operation of insurance institution is often affected by random environment, potential opportunity cost of capital or inflation. Considering this phenomenon, this paper establishes a new Markovian environment compound binomial risk model with capital cost, abbreviated as RMCM model. The new RMCM model is a complex recursive model which is difficult to calculate. To calculate the results in many future periods at one time, it is necessary to design an algorithm that can greatly improve calculation efficiency. One of the aims of this study is to conduct an analysis of the recursive algorithm, divide and conquer strategy and other algorithm theories to, designs a new MCPRAM-algorithm that is able to solve the calculation of this kind of recursive model with high complexity, multiple cycles and multiple periods, significantly improving the practical application value of the actuarial model. Taking aviation accident insurance as an example, the measurement methods of actuarial quantity in the model are explained statistically, and the calculation algorithm of conditional ruin probability is elaborated in detail. The conditional ruin probabilities of 60 periods under different operating conditions and different environment states were obtained and then compared and analyzed. RMCM has a wide range of applications and is suitable for describing the insurance products with low premium, small compensation probability; large claim amount and one-off compensation in a random market environment. The RMCM model proposed in this paper clarifies the risk of insurance institutions, compares the calculation of seven groups of parameter data, and obtains better parameters to control the bankruptcy risk at about 5% in the next five years. Parameter data reference and MCPRAM-algorithm can be used to design and develop new insurance products in a random environment, and provide valuable decision support for the scientific operation and management of insurance institutions.

Suggested Citation

  • XIAO, Lin, 2022. "Compound binomial risk model in a Markovian environment with capital cost and the calculation algorithm," Applied Mathematics and Computation, Elsevier, vol. 424(C).
    • Handle: RePEc:eee:apmaco:v:424:y:2022:i:c:s0096300322000558
    DOI: 10.1016/j.amc.2022.126969
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322000558
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.126969?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gerber, Hans U., 1988. "Mathematical fun with ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 7(1), pages 15-23, January.
    2. Reinhard, Jean-Marie, 1984. "On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment," ASTIN Bulletin, Cambridge University Press, vol. 14(1), pages 23-43, April.
    3. Cossette, Helene & Landriault, David & Marceau, Etienne, 2004. "Compound binomial risk model in a markovian environment," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 425-443, October.
    4. Willmot, Gordon E., 1993. "Ruin probabilities in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 12(2), pages 133-142, April.
    5. J.M. Reinhard, & Snoussi, M., 2001. "On the Distribution of the Surplus Prior to Ruin in a Discrete Semi-Markov Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 31(2), pages 255-273, November.
    6. Cheng, Shixue & Gerber, Hans U. & Shiu, Elias S. W., 2000. "Discounted probabilities and ruin theory in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 239-250, May.
    7. Gerber, Hans U., 1988. "Mathematical Fun with the Compound Binomial Process," ASTIN Bulletin, Cambridge University Press, vol. 18(2), pages 161-168, November.
    8. Jae-Kyung Woo & Haibo Liu, 2018. "Discounted Aggregate Claim Costs Until Ruin in the Discrete-Time Renewal Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1285-1318, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yang, Hu & Zhang, Zhimin & Lan, Chunmei, 2009. "Ruin problems in a discrete Markov risk model," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 21-28, January.
    2. Chen, Mi & Yuen, Kam Chuen & Guo, Junyi, 2014. "Survival probabilities in a discrete semi-Markov risk model," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 205-215.
    3. Palmowski, Zbigniew & Ramsden, Lewis & Papaioannou, Apostolos D., 2024. "Gerber-Shiu theory for discrete risk processes in a regime switching environment," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    4. Marceau, Etienne, 2009. "On the discrete-time compound renewal risk model with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 245-259, April.
    5. Li, Shuanming & Garrido, José, 2002. "On the time value of ruin in the discrete time risk model," DEE - Working Papers. Business Economics. WB wb021812, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    6. Pavlova, Kristina P. & Willmot, Gordon E., 2004. "The discrete stationary renewal risk model and the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 267-277, October.
    7. Bao, Zhenhua & Song, Lixin & Liu, He, 2013. "A note on the inflated-parameter binomial distribution," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1911-1914.
    8. Liu, Guoxin & Zhao, Jinyan, 2007. "Joint distributions of some actuarial random vectors in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 95-103, January.
    9. Jae-Kyung Woo & Haibo Liu, 2018. "Discounted Aggregate Claim Costs Until Ruin in the Discrete-Time Renewal Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1285-1318, December.
    10. Claude Lefèvre & Stéphane Loisel, 2008. "On Finite-Time Ruin Probabilities for Classical Risk Models," Post-Print hal-00168958, HAL.
    11. Constantinescu Corina D. & Kozubowski Tomasz J. & Qian Haoyu H., 2019. "Probability of ruin in discrete insurance risk model with dependent Pareto claims," Dependence Modeling, De Gruyter, vol. 7(1), pages 215-233, January.
    12. Cossette, Helene & Landriault, David & Marceau, Etienne, 2004. "Exact expressions and upper bound for ruin probabilities in the compound Markov binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 449-466, June.
    13. David Landriault, 2008. "On a generalization of the expected discounted penalty function in a discrete‐time insurance risk model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(6), pages 525-539, November.
    14. Liu, Guoxin & Wang, Ying & Zhang, Bei, 2005. "Ruin probability in the continuous-time compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 303-316, June.
    15. S. X. Liu & J. Y. Guo, 2006. "Discrete Risk Model Revisited," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 303-313, June.
    16. Tan, Jiyang & Yang, Xiangqun, 2006. "The compound binomial model with randomized decisions on paying dividends," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 1-18, August.
    17. Kam Pui Wat & Kam Chuen Yuen & Wai Keung Li & Xueyuan Wu, 2018. "On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends," Risks, MDPI, vol. 6(1), pages 1-13, January.
    18. Cossette, Helene & Landriault, David & Marceau, Etienne, 2004. "Compound binomial risk model in a markovian environment," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 425-443, October.
    19. Dutang, C. & Lefèvre, C. & Loisel, S., 2013. "On an asymptotic rule A+B/u for ultimate ruin probabilities under dependence by mixing," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 774-785.
    20. Cheng, Shixue & Gerber, Hans U. & Shiu, Elias S. W., 2000. "Discounted probabilities and ruin theory in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 239-250, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:424:y:2022:i:c:s0096300322000558. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.