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On the compound binomial risk model with stochastic income. (English) Zbl 1297.62215

Summary: In this paper we consider a risk model where both premiums and claims follow compound binomial processes. A difference equation and a defective renewal equation satisfied respectively by the expected discounted penalty function are derived. Then for a special penalty function and geometrically distributed claim amounts, an explicit expression of the expected discounted penalty function is obtained. Finally, we investigate the case when premiums are degenerate at a constant amount. We derive an alternative defective renewal equation in terms of the roots of the generalized Lundberg’s fundamental equation.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
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