Unlocking Reserve Assumptions Based on the Retrospective Loss Random Variable

In this paper, we define a retrospective loss random variable and mathematically demonstrate that its expectation is the retrospective reserve which in turn is equivalent to the prospective reserve. By defining an associated random variable for the retrospective reserve, similar to the prospective loss random variable for the prospective reserve, we can further explore and understand various properties of this retrospective loss random variable. In particular, we find and demonstrate that this retrospective random variable can be a powerful tool for providing us valuable historical information on the pattern and significance of deviation of actual experience from that assumed for reserving purposes. This valuable information can subsequently guide us as to whether it becomes necessary to adjust prospective reserves and the procedure to do so. The paper concludes with a model of a block of in force policies with actual experience different from reserving assumptions, and a rigorous and consistent methodology on how prospective reserves could be adjusted based on the realized retrospective loss random variable