Journal of Mathematics and Statistics

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

Juma Kasozi, Fred Mayambala and Charles Wilson Mahera

DOI : 10.3844/jmssp.2011.61.67

Journal of Mathematics and Statistics

Volume 7, Issue 1

Pages 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.

Copyright

© 2011 Juma Kasozi, Fred Mayambala and Charles Wilson Mahera. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.