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

Journal of Mathematics and Statistics

Juma Kasozi¹  Fred Mayambala¹  Charles W. Mahera¹ 

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

DOI  :  10.3844/jmssp.2011.61.67

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

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

【 授权许可】

Unknown