Stochastic Models for Continuing Care Retirement Communities

Continuing care retirement communities (CCRCs) offer housing and a variety of services, including long-term care. Typically, the cost of this long-term care is wholly or partially covered by entry and/or periodic fees. Thus, CCRCs provide a long-term-care insurance benefit. For this and other reasons, actuarial involvement in the financial management of CCRCs is desirable. To carry out actuarial analyses of CCRCs, appropriate models are required to describe the status of individual residents and the CCRC population.This paper presents models that assume that, at any time, a resident is in a given “state,” which is determined by the individual’s care requirements. The resident may make “transitions” between states at various times, and randomness is associated with both the transition times and the states entered. Actuarial calculations using such a model are discussed, and numerical illustrations are provided. A simple model is examined first; then generalizations are considered. The model for an individual resident can be embedded in a model for a CCRC population. This is explored with particular attention given to the “high-demand” situation in which potential residents are always waiting to enter the community. With this model, the goal is to analyze the future care requirements of the CCRC population.