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<p>Inspired by a duration-dependent life insurance model, we consider continuous-time semi-Markov jump processes, initially assumed to have a finite state space. We develop approximations using jump processes that are time-homogeneous Markov when conditioned on a high-intensity Poissonian grid (grid-conditionally). Our results are based on a recent adaptation of the uniformisation principle which yields a strongly pathwise convergent sequence of jump processes. In contrast to traditional methods that use classical approximations to integro–differential equation solutions to compute value functions, our approximations result in easily implementable expressions, making them valuable in situations where evaluating pathwise distributional functionals for the original semi-Markov process is challenging. Our homogeneous approximation, initially grid-conditional, evolves into an unconditional version that remains effective under reasonable regularity assumptions. We then relax the finite-state-space assumption and show how our results can be extended to a general measurable state space. We illustrate the practicality of our approach with a disability insurance model, using realistic underlying semi-Markov process parameters.</p>

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Approximations of semi-Markov processes and insurance policy valuation

  • 期刊论文

  • 发表日期：

    2025年10月9日

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  • Martin Bladt,
  • Andreea Minca,
  • Oscar Peralta

摘要

Inspired by a duration-dependent life insurance model, we consider continuous-time semi-Markov jump processes, initially assumed to have a finite state space. We develop approximations using jump processes that are time-homogeneous Markov when conditioned on a high-intensity Poissonian grid (grid-conditionally). Our results are based on a recent adaptation of the uniformisation principle which yields a strongly pathwise convergent sequence of jump processes. In contrast to traditional methods that use classical approximations to integro–differential equation solutions to compute value functions, our approximations result in easily implementable expressions, making them valuable in situations where evaluating pathwise distributional functionals for the original semi-Markov process is challenging. Our homogeneous approximation, initially grid-conditional, evolves into an unconditional version that remains effective under reasonable regularity assumptions. We then relax the finite-state-space assumption and show how our results can be extended to a general measurable state space. We illustrate the practicality of our approach with a disability insurance model, using realistic underlying semi-Markov process parameters.