Browsing by Author "Mayambala, Fred"

Now showing 1 - 2 of 2
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    Controlling Ultimate Ruin Probability by Quota-Share Reinsurance Arrangements
    (2013) Kasozi, Juma; Charles, Wilson M.; Mayambala, Fred
    A basic insurance model is perturbated by a diffusion. We take this model to represent the wealth dynamics of an insurance company. The model is compounded by another return on investments process of the Black-Scholes type. Both models form the risk process used in this work. Further, to manage her risk levels, the company enters into quota-share reinsurance arrangements with a reinsurer. We derive a second-order Volterra integro-differential equation which we transforminto a linear Volterra integral equation of the second kind. We have solved the equations numerically using the block-by-block method for different retention levels for the chosen parameters. Results show that quota-share reinsurance improves the survival of the insurer
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    Dividend Maximization in the Cramer-Lundberg Model using Homotopy Analysis Method
    (2011) Kasozi, Juma; Mayambala, Fred; Charles, Wilson M.
    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.