Approximations of semi-Markov processes and insurance policy valuation
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915433935798272 |
|---|---|
| author | Bladt, Martin Minca, Andreea Peralta, Oscar |
| author_facet | Bladt, Martin Minca, Andreea Peralta, Oscar |
| contents | 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, conditioned on a high-intensity Poissonian grid (grid-conditional). Our results are based on a recent adaptation of the uniformization 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06784 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Approximations of semi-Markov processes and insurance policy valuation Bladt, Martin Minca, Andreea Peralta, Oscar Probability 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, conditioned on a high-intensity Poissonian grid (grid-conditional). Our results are based on a recent adaptation of the uniformization 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. |
| title | Approximations of semi-Markov processes and insurance policy valuation |
| topic | Probability |
| url | https://arxiv.org/abs/2312.06784 |