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) |