Our projections indicate that over a lifetime, the risk of entering a nursing home and spending a long time there is substantial. With the elderly population growing, this has important implications for both medical practice and the financing of long-term care.

We present new algorithms for the solution of large structured Markov models whose in nitesimal generator can be expressed as a Kronecker expression of sparse matrices. We then compare them with the shu e-based method commonly used in this context and show how our new algorithms can be advantageous in dealing with very sparse matrices and in supporting both Jacobi-style and Gauss-Seidel-style methods with appropriate multiplication algorithms. Our main contribution is to show how solution algorithms based on Kronecker expression can be modi ed to consider probability vectors of size equal to the \actual" state space instead of the \potential" state space, thus providing space and time savings. The complexity of our algorithms is compared under di erent sparsity assumptions. A nontrivial example is studied to illustrate the complexity of the implemented algorithms.

No abstract

These findings provide support for many of the management-practice improvements taking place in the field, including those implemented in the BJBC demonstration. Follow-up surveys will provide insight into their effectiveness.

The leading edge of the baby boom generation is nearing retirement and facing uncertainty about its need for long-term care (LTC). Using a microsimulation model, this analysis projected that people currently turning age 65 will need LTC for three years on average. An important share of needed care will be covered by public programs and some private insurance, but much of the care will be an uninsured private responsibility of individuals and their families-a responsibility that will be distributed unequally. While over a third of those now turning 65 are projected to never receive family care, three out of 10 will rely on family care for more than two years. Similarly, half of people turning 65 will have no private out-of-pocket expenditures for LTC, while more than one in 20 are projected to spend $100,000 or more of their own money (in present discounted value). Policy debate that focuses only on income security and acute care-and the corresponding Social Security and Medicare programs-misses the third, largely private, risk that retirees face: that of needing LTC.