A change of variable formula with applications to multi-dimensional optimal stopping problems

Cheng Cai and Tiziano De Angelis

Stochastic Processes and their Applications, 2023, vol. 164, issue C, 33-61

Abstract: We derive a change of variable formula for C1 functions U:R+×Rm→R whose second order spatial derivatives may explode and not be integrable in the neighbourhood of a surface b:R+×Rm−1→R that splits the state space into two sets C and D. The formula is tailored for applications in problems of optimal stopping where it is generally very hard to control the second order derivatives of the value function near the optimal stopping boundary. Differently to other existing papers on similar topics we only require that the surface b be monotonic in each variable and we formally obtain the same expression as the classical Itô’s formula.

Keywords: Itô’s formula; Change of variable formula; Multidimensional optimal stopping (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414923001400
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:164:y:2023:i:c:p:33-61

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.2023.07.005

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 ().