Using an approach similar to that of Gerber and Shiu (1998), a recursive formula is given for the expected discounted penalty due at ruin, in the discrete time risk model. With it the joint distribution of three random variables is obtained; time to ruin, the surplus just before ruin and the...

Non-homogenous Poisson processes with periodic claim intensity rate are proposed as the claim counting process of risk theory. We introduce a doubly periodic Poisson model with short and long term trends, illustrated by a double-beta intensity function. Here periodicity does not repeat the exact...

Risk classification is an important part of the actuarial process in Insurance companies. It allows for the underwriting of the best risks, through an appropriate choice of classification variables, and helps set fair premiums in rate-making. Logistic regression is one of the sophisticated...