Metraipolis › archive › dc_ed6200c141aa

Risk diversification for infinitely divisible distributions — arXiv:2609.25452

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.25452
License (as archived): CC0-1.0
Archived: 2026-10-08T15:54:21.788Z
SHA-256 of the archived text: 23aa203be1ac50ca082badf90cb797164ee45e6468a2d733bc7dae6ffb8313b9
Stable URL of this page: https://metraipolis.com/documento/dc_ed6200c141aa

How to cite

Risk diversification for infinitely divisible distributions — arXiv:2609.25452 — arXiv (en), https://arxiv.org/abs/2609.25452 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ed6200c141aa (Metraipolis archive dc_ed6200c141aa, sha256 23aa203be1ac50ca082badf90cb797164ee45e6468a2d733bc7dae6ffb8313b9)

BibTeX

@misc{dced6200c141aa,
  title = {Risk diversification for infinitely divisible distributions — arXiv:2609.25452},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.25452},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ed6200c141aa; sha256 23aa203be1ac50ca082badf90cb797164ee45e6468a2d733bc7dae6ffb8313b9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.25452. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In this paper, we study the diversification properties of convex combinations of iid infinitely divisible random variables. For Lévy processes with bounded variation sample paths, we characterize, in terms of subadditivity and concavity of the transformed Lévy tails, Lévy processes that exhibit the non-diversification phenomenon or the reverse diversification order with respect to the majorization order uniformly over all time horizons. For general symmetric Lévy processes without a Gaussian component, we show that the symmetric 1-stable Lévy process is the only nontrivial process exhibiting either phenomenon. We further investigate convex combinations of components of multivariate infinitely divisible distributions, allowing for dependent and heterogeneous components, and characterize the Lévy measures of multidimensional Lévy processes exhibiting the two adverse diversification phenomena uniformly over all time horizons. Explicit characterizations are obtained for the multidimensional symmetric Lévy processes, multidimensional $\alpha$-stable processes and multidimensional compound Poisson processes. Finally, we show that the non-diversification phenomenon extends beyond Lévy processes to running maxima and integrals of increasing convex functionals of Lévy processes, while both adverse diversification phenomena are preserved for Lévy-driven stochastic integrals with nonnegative deterministic kernels. Applications to ruin theory, storage processes and stochastic volatility are also discussed.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-23 in math.PR).
Categorie arXiv: Probability (math.PR) ; Risk Management (q-fin.RM).
Pagina del lavoro: https://arxiv.org/abs/2609.25452 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T15:13:13.513Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-23?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).