Convex ordering for stochastic Volterra equations and their Euler schemes

Benjamin Jourdain () and Gilles Pagès ()
Additional contact information
Benjamin Jourdain: INRIA
Gilles Pagès: Sorbonne Université

Finance and Stochastics, 2025, vol. 29, issue 1, No 1, 62 pages

Abstract: Abstract In this paper, we are interested in comparing solutions to stochastic Volterra equations for the convex order on the space of continuous R d ${\mathbb{R}}^{d}$ -valued paths and for the monotonic convex order when d = 1 $d=1$ . Even if these solutions are in general neither semimartingales nor Markov processes, we are able to exhibit conditions on their coefficients enabling the comparison. Our approach consists in first comparing their Euler schemes and then taking the limit as the time step vanishes. We consider two types of Euler schemes, depending on the way the Volterra kernels are discretised. The conditions ensuring the comparison are slightly weaker for the first scheme than for the second, and this is the other way around for convergence. Moreover, we weaken the integrability needed on the starting values in the existence and convergence results in the literature to be able to only assume finite first moments, which is the natural framework for convex ordering.

Keywords: Stochastic Volterra equations; Quadratic rough Heston model; Convex order; Euler schemes; 60E15; 60F15; 60G22; 91G30 (search for similar items in EconPapers)
JEL-codes: C63 G10 G12 (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00780-024-00551-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:finsto:v:29:y:2025:i:1:d:10.1007_s00780-024-00551-3

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

DOI: 10.1007/s00780-024-00551-3

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().