  This paper examines the retirement decision, optimal investment, and
consumption strategies under an age-dependent force of mortality. We formulate
the optimization problem as a combined stochastic control and optimal stopping
problem with a random time horizon, featuring three state variables: wealth,
labor income, and force of mortality. To address this problem, we transform it
into its dual form, which is a finite time horizon, three-dimensional
degenerate optimal stopping problem with interconnected dynamics. We establish
the existence of an optimal retirement boundary that splits the state space
into continuation and stopping regions. Regularity of the optimal stopping
value function is derived and the boundary is proved to be Lipschitz
continuous, and it is characterized as the unique solution to a nonlinear
integral equation, which we compute numerically. In the original coordinates,
the agent thus retires whenever her wealth exceeds an age-, labor income- and
mortality-dependent transformed version of the optimal stopping boundary. We
also provide numerical illustrations of the optimal strategies, including the
sensitivities of the optimal retirement boundary concerning the relevant
model's parameters.
