Markov projection of semimartingales — Application to comparison results

Benedikt Köpfer and Ludger Rüschendorf

Stochastic Processes and their Applications, 2023, vol. 162, issue C, 361-386

Abstract: In this paper we derive generalizations of comparison results for semimartingales. Our results are based on Markov projections and on known comparison results for Markov processes. The first part of the paper is concerned with an alternative method for the construction of Markov projections of semimartingales. In comparison to the construction in Bentata and Cont (2009) which is based on the solution of a well-posed martingale problem, we make essential use of pseudo-differential operators as investigated in Böttcher (2008) and of fundamental solutions of related evolution problems. This approach allows to dismiss with some boundedness assumptions on the differential characteristics in the martingale approach. As consequence of the construction of Markov projections, comparison results for path-independent functions (European options) of semimartingales can be reduced to the well investigated problem of comparison of Markovian semimartingales. The Markov projection approach to comparison results does not require one of the semimartingales to be Markovian, which is a common assumption in literature. An idea of Brunick and Shreve (2013) to mimick updated processes leads to a related reduction result to the Markovian case and thus to the comparison of related generators. As consequence, a general comparison result is also obtained for path-dependent functions of semimartingales.

Keywords: Markov projection; Pseudo-differential operators; Ordering of semimartingales (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414923000923
Full text for ScienceDirect subscribers only

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:eee:spapps:v:162:y:2023:i:c:p:361-386

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2023.04.018

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().