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An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company

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  • Soontorn Boonta
  • Somchit Boonthiem

Abstract

Catastrophe is a loss that has a low probability of occurring but can lead to high‐cost claims. This paper uses the data of fire accidents from a reinsurance company in Thailand for an experiment. Our study is in two parts. First, we approximate the parameters of a Weibull distribution. We compare the parameter estimation using a direct search method with other frequently used methods, such as the least squares method, the maximum likelihood estimation, and the method of moments. The results show that the direct search method approximates the parameters more precisely than other frequently used methods (to four‐digit accuracy). Second, we approximate the minimum initial capital (MIC) a reinsurance company has to hold under a given ruin probability (insolvency probability) by using parameters from the first part. Finally, we show MIC with varying the premium rate.

Suggested Citation

  • Soontorn Boonta & Somchit Boonthiem, 2019. "An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company," Journal of Applied Mathematics, John Wiley & Sons, vol. 2019(1).
    • Handle: RePEc:wly:jnljam:v:2019:y:2019:i:1:n:2191509
    DOI: 10.1155/2019/2191509
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    References listed on IDEAS

    as
    1. Wai-Sum Chan & Lianzeng Zhang, 2006. "Direct Derivation of Finite-Time Ruin Probabilities in the Discrete Risk Model with Exponential or Geometric Claims," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 269-279.
    2. Chengguo Weng & Yi Zhang & Ken Tan, 2009. "Ruin probabilities in a discrete time risk model with dependent risks of heavy tail," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2009(3), pages 205-218.
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