A Unifying Approach to the Ruin Problems Under the Compound Binomial Model

Abstract

In this paper, the aggregate claims are modeled as a compound binomial process and the individual claim sizes are integer-valued. Taking advantage of the expected discounted penalty function, we derive, when a discount factor$\nu$is taken into account, the recursive formulas, generating functions, defective renewal equations, asymptotic expression and explicit expressions for some quantities related to the ruin. We indicate that the maximal aggregate loss of the surplus process can be expressed as a compound geometric random variable, whose tail is exactly the generating function of the ruin time.