Research Article Open Access

Dividend Maximization in the Cramer-Lundberg Model using Homotopy Analysis Method

Juma Kasozi1, Fred Mayambala1 and Charles Wilson Mahera2
  • 1 ,
  • 2 , Afganistan
Journal of Mathematics and Statistics
Volume 7 No. 1, 2011, 61-67

DOI: https://doi.org/10.3844/jmssp.2011.61.67

Submitted On: 18 November 2010 Published On: 31 January 2011

How to Cite: Kasozi, J., Mayambala, F. & Mahera, C. W. (2011). Dividend Maximization in the Cramer-Lundberg Model using Homotopy Analysis Method. Journal of Mathematics and Statistics, 7(1), 61-67. https://doi.org/10.3844/jmssp.2011.61.67

Abstract

Problem statement: We used the Homotopy Analysis Method (HAM) to numerically compute the value function of the dividend payment in the basic insurance process. Approach: The process is a constant income stream from premiums which is subtracted a claim process of the Poisson type. Further, an allowance for payment of dividends to share holders was incorporated. Results: The case when the claims are exponential has an analytical solution. The HAM was then applied to the resulting Hamilton-Jacobi-Bellman equation and the numerical results obtained were compared to the theoretical results in order to check the validity of the method. Conclusion: The HAM was then applied to the model to check for other claim size distributions. The results obtained are very encouraging.

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Keywords

  • Cramer-Lundberg model
  • hamilton-jacobi-bellman equation
  • dividends
  • barrier strategy
  • Homotopy Analysis Method (HAM)
  • Expected Present Value (EPP)