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Title: Discounted lifetime cost of post-retirement long-term care and annuity benefits under Markov mortality-morbidity models Authors:  Colin Ramsay - University of Nebraska-Lincoln (United States) [presenting]
Victor Oguledo - Florida A and M University (United States)
Abstract: Suppose for individuals with health risk parameter $\theta$, their health state can be modeled as continuous time Markov processes, $\{Z(t,\theta), t \geq 0\}$, with state space $S=\{1,2,\ldots,m\}$. Assume higher values of $\theta$ and $S$ denote less healthy individuals and worse health states, respectively. There is one death state: $m$. Individuals get random health shocks then seek long term care. Let $\alpha >0$ be the level quality of care received, with higher values of $\alpha$ denoting higher quality of care. Let $C_{j}(t,\theta,\alpha)$ denote the cost of care at time $t$ for individuals in state $j$ with risk parameter $\theta$ and quality of care $\alpha$, with $C_{j}(t,\theta,\alpha)$ being non-decreasing in $t$, $\theta$, and $\alpha$. We assume the transition intensities of $Z(t,\theta)$ are time homogeneous and depend on the quality of care being provided. Using publicly available estimates of $C_{j}(t,\theta,\alpha)$ and transition intensities, we construct a time homogeneous Markov chain with transition intensities depending only on $\theta$ and $\alpha$ according to a quasi-frailty model. Transition probabilities are found using uniformization algorithms. We then determine the expected discounted lifetime cost of post-retirement long-term care and annuity benefits for various values of $\theta$ and $\alpha$. For a given lifetime budget constraint, we determine the optimal value of $\alpha$ for given $\theta$ using the Nelder-Mead simplex algorithm.