Stochastic models for long-term car

The aging population has created many questions and concerns regarding the long-term of the elderly. Careful planning will be required to deliver and finance services within a cost-effective long-term care system.;An integral part of this planning process is the analysis of future care needs and associated costs. Stochastic models are ideal for examining the future care requirements of both a single individual and the population in total. Not only do these models permit the projection of future needs and costs, but they provide information on the potential variation in these quantities.;This thesis develops stochastic models for analyzing long-term care in both an individual and a group setting. The focus is on obtaining distributional results for the various quantities of interest.;Chapter 2 explores multi-state models which may be used in modelling the care requirements of an individual. The states represent the several levels of care. Semi-Markov and Markov models are considered. Their properties are outlined and useful techniques and results are discussed.;An analysis of long-term care costs is presented in Chapter 3. A five-state model involving three levels of care is used. Model parameters are estimated from actual data based on a time-homogeneous Markov assumption. The results are then used to examine the distribution of the present value of future costs for an individual.;Chapter 4 investigates open group long-term care models. Here a community of individuals is considered. Elderly persons are assumed to enter the community according to a nonhomogeneous Poisson process. They then move amongst the care requirement states according to some process. Distributional results are obtained for the future population in each state, the future annual cost and the present value of future costs.;Open group models involving limited resources are addressed in Chapter 5. The distribution of the shortage in resources is examined. A suggested cost structure then allows resources to be allocated so that expected costs are minimized. A model for continuing care retirement communities is also analyzed.