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THE MIXED NEGATIVE BINOMIAL PROCESS RISK MODEL WITH SMALL CLAIMS STOCHASTIC PROCESS AND RUIN PROBABILITY

ABSTRACT
If the random variable changes with time, we can consider it a stochastic process. The stochastic claims process is particularly important in insurance, where the frequency of claims is a random variable. Classical risk models typically assume that the number of claims by insurance companies follows an (a, b, 0) type distribution. In practice, however, the number of claims is often an over-dispersed or heavy-tailed phenomenon. To compensate for this deficiency, mixed distributions have been proposed. This article discusses the lapse probability of a general compound mixed negative binomial small claims process risk model based on a negative binomial mixture distribution.
KEYWORDS
PAPER SUBMITTED: 2023-07-21
PAPER REVISED: 2024-05-07
PAPER ACCEPTED: 2024-05-07
PUBLISHED ONLINE: 2025-07-06
DOI REFERENCE: https://doi.org/10.2298/TSCI2503041Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2025, VOLUME 29, ISSUE Issue 3, PAGES [2041 - 2049]
REFERENCES
  1. He, J.-H., Qian, M. Y., A Fractal Approach to the Diffusion Process of Red Ink in a Saline Water, Thermal Science, 26 (2022), 3, pp. 2447-2451
  2. Embrechts, P., et al., Modelling Extremal Events for Insurance and Finance, Springer, Berlin, Germany, 1997
  3. Rolski, T., et al., Stochastic Processes for Insurance and Finance, Wiley & Sons., New York, USA, 1999
  4. Hipp, C., Asymptotics of Ruin Probabilities for Controlled Risk Processes in the Small Claims Case, Scandinavian Actuarial Journal, 2004 (2004), 5, pp. 321-335
  5. Grigori, J., Approximation of Ruin Probability and Ruin Time in Discrete Brownian Risk Models, Scandinavian Actuarial Journal, 2020 (2020), 8, pp. 718-735
  6. Albrecher, H., et al., Efficient Simulation of Ruin Probabilities When Claims are Mixtures of Heavy and Light Tails, Methodology and Computing in Applied Probability, 23 (2021), 4, pp. 1237-1255
  7. Emillio, G. D., et al., Univariate and Multivariate Versions of the Negative Binomial Inverse Gaussian Distributions with Applications, Insurance: Mathematics and Economics, 42 (2008), 1, pp. 39-49
  8. Chookait, P., et al., A New Mixed Negative Binomial Distribution, Journal of Applied Sciences, 12 (2012), 17. pp. 1853-1858
  9. Gencturk, Y., Yigiter, A., Modelling Claim Number Using a New Mixture Model: Negative Binomial Gamma Distribution, Journal of Statistical Computation and Simulation, 86 (2016), 10, pp. 1829-1839
  10. Sirinapa, A., The Negative Binomial Generalized Exponential Distribution, Applied Mathematical Sciences, 7 (2013), 22, pp. 1093-1105
  11. Ahmad, I. S., et al., Negative Binomial Reciprocal Inverse Gaussian Distribution: Statistical Properties with Applications, Statistics, 19 (2021), 3, pp. 437-449

2025 Society of Thermal Engineers of Serbia. Published by the VinĨa Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence