In this article, we consider the generalized Erlang risk model and its dual model. By using a conditional measure-preserving correspondence between the two models, we derive an identity for two interesting conditional probabilities. Applications to the discounted joint density of the surplus prior to ruin and the deficit at ruin are also discussed.

he oil industry was among the first of the large industries both to adopt discounted cash flow methods in valuing assets and projects. Discounted cash flow (DCF) tools are fundamental to engineering and financial analysis in the oil industry. They are well understood by managers and generally provide accurate valuations of developed hydrocarbon reserves. Unfortunately, DCF techniques systematic...

We assume that consumer demand for an item follows a Brownian motion with a drift that is modulated by a continuous-time Markov chain that represents the regime of the economy. The economy may be in either one of two regimes. The economy remains in one regime for a random amount of time that is exponentially distributed with rate λ1, and then moves to the other regime and remains there an expon...