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Controlling Ultimate Ruin Probability by Quota-share Reinsurance Arrangements

Juma Kasozi, Charles Wilson Mahera, Fred Mayambala


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


Ultimate Ruin probability, HJB equation, Volterra equations, Block-by-block method, Quota-share reinsurance.

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