Title: Optimal design of long term care insurance for Medicaid seniors using a multi-state Markov model of mortality/morbidity
Authors: Colin Ramsay - University of Nebraska-Lincoln (United States) [presenting]
Victor Oguledo - Florida A and M University (United States)
Abstract: Consider a retired U.S. senior (i.e., a retiree age 65 or older) who is eligible for some degree of help from Medicaid (which is a US federal/state government social welfare program). The retiree desires lifetime income and is concerned about health shocks that can lead to long term care, which is very expensive in the U.S. We assume that the retiree has a lump sum amount of $G$ to buy a life annuity and pay for long term care. We explore the optimal design of a life annuity plus a long term care insurance rider to pay for long term care services and supports. To this end, we assume there are four stakeholders: (i) the retiree who wants to maximize her expected utility and minimize her out-of-pocket expenses, (ii) the long term care provider who wants to maximize its profits, (iii) Medicaid that wants to minimize its payments for long term care, and (iv) the insurer who wants to charge an actuarially sound premium. We develop the optimal design by constructing two sets of two dimensional multi-objective optimization problems. From the first set of optimization problems, the long term care provider and Medicaid provide the retiree with a set of policies along their Pareto frontier. Under the second set of optimization problems, the retiree creates her own Pareto frontier to make her optimal choice. An illustrative example is provided.