Description: This is a sequel to author's earlier paper on Installment Premiums. This paper explores the parallel case of apportionable premiums, another situation in which a special adjustment payment at death causes an otherwise somewhat complex policy to be identical with a more simple and familiar one. As with installment premiums, this will result in terminal reserves for the complex policy being exactly equal to those for its corresponding familiar policy.

Description: This paper builds a new risk model for a firm which is sensitive to its credit quality. A modified Jarrow, Lando and Turnball model [Markov Chain model] is used to model the credit rating. Recursive equations for finite time ruin probability and distribution of ruin time are derived. Coupled Volterra type integral equation systems for ultimate ruin probability, severity of ruin and joint distribution of surplus before and after ruin are also obtained. Some numerical results are included.

Description: This paper deals with how the credibility levels change based on this lack knowledge. Group insuraace models are used, bill some of tile techniques could apply to any insurance risk.

Description: In this paper we discuss some properties of the nth stop-loss order and their application in risk premium principles. We give a necessary condition and a sufficient condition for nth stop-loss orders. They are convenient tools to construct risk pairs with nth stop-loss orders. We show that exponential premium principles can diferentiate between losses more finely than the net premium principles under some conditions.