@article {10.3844/jmssp.2011.61.67, article_type = {journal}, title = {Dividend Maximization in the Cramer-Lundberg Model using Homotopy Analysis Method}, author = {Kasozi, Juma and Mayambala, Fred and Mahera, Charles Wilson}, volume = {7}, year = {2011}, month = {Jan}, pages = {61-67}, doi = {10.3844/jmssp.2011.61.67}, url = {https://thescipub.com/abstract/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.}, journal = {Journal of Mathematics and Statistics}, publisher = {Science Publications} }