On the forward rate concept in multi-state life insurance

Forward transition rates

“…actuarial practitioners searching for simple benchmark models. A similar way of thinking in a slightly different framework drives the work of Christiansen and Niemeyer [6]. We provide a substantiating example at the end of this subsection.…”

“…Another part of our contribution is the establishment of a theoretical framework for the discussion and comparison of forward rate definitions. This allows us to give a clear presentation of the relation between the different suggestions pushed forward by Christiansen and Niemeyer [6], Buchardt [4], and this paper, and a highlight of the pros and cons of each idea. Our conclusion is different from the negative of Norberg [19].…”

“…In addition to the work of Norberg [19], the question has also been investigated by e.g. Christiansen and Niemeyer [6] and Buchardt [4].…”

“…Hereby, they show that if one desires 'universal' forward transitions rates that solely rely on the probabilistic structure of µ, such as the marginal forward transition rates, one must assume a specific and often unrealistic dependency structure between the transitions rates, see e.g. Christiansen and Niemeyer [6] paragraph following Remark 5.5. If instead one is solely interested in sojourn payments and willing to specify a specific structure of the jump process X, the forward equations rates provide a natural alternative not confined to a specific dependency structure between the transition intensities.…”

“…As it turned out, this was not enough to kill the idea itself. Lately, Christiansen and Niemeyer [6] and Buchardt [4] have proposed different generalizations with individual characteristics.…”