Assessing continuous common-shock risk through matrix distributions
Abstract
We introduce a class of continuous-time bivariate phase-type distributions for modeling dependencies from common shocks. The construction uses continuous-time Markov processes that evolve identically until an internal common-shock event, after which they diverge into independent processes. We derive and analyze key risk measures for this new class, including joint cumulative distribution functions, dependence measures, and conditional risk measures. Theoretical results establish analytically tractable properties of the model. For parameter estimation, we employ efficient gradient-based methods. Applications to both simulated and real-world data illustrate the ability to capture common-shock dependencies effectively. Our analysis also demonstrates that common-shock continuous phase-type distributions may capture dependencies that extend beyond those explicitly triggered by common shocks.
Cite
@article{arxiv.2507.15637,
title = {Assessing continuous common-shock risk through matrix distributions},
author = {Martin Bladt and Oscar Peralta and Jorge Yslas},
journal= {arXiv preprint arXiv:2507.15637},
year = {2025}
}