On a risk model with stochastic premiums income and dependence between income and loss

Labbé and Sendova (2009) [9] consider a compound Poisson risk model with stochastic premiums income. In this paper, we extend their model by assuming that there exists a specific dependence structure among the claim sizes, interclaim times and premium sizes. Assume that the distributions of the premium sizes and interclaim times are controlled by the claim sizes. When the individual premium sizes are exponentially distributed, the Laplace transforms and defective renewal equations for the (Gerber–Shiu) discounted penalty functions are obtained. When the individual premium sizes have rational Laplace transforms, we show that the Laplace transforms for the discounted penalty functions can also be obtained.