  Continuous-time semi-Markov finite state-space jump processes are considered,
inspired by a duration-dependent life insurance model. New approximations using
grid-conditional homogeneous Markov jump-processes are developed, based on a
recent adaptation of the uniformization principle which results in a strong
pathwise convergent sequence of jump processes. Unlike traditional methods that
use classical approximations to integro-differential equation solutions to
compute their value functions, the proposed grid-conditional homogeneous Markov
jump-processes allows for a direct and tractable approximation. In particular,
these approximations simplify to easily implementable expressions, making them
useful in areas where evaluating pathwise distributional functionals is
difficult. Our homogeneous approximation, initially of a grid-conditional kind,
is evolved into an unconditional version that holds well under fair regularity
assumptions. The practicality of this approach is demonstrated on a disability
life insurance model, with realistic underlying semi-Markov process parameters,
showcasing its broader applicability in operations research and related fields.
