A Class of Itô Diffusions with Known Terminal Value and Specified Optimal Barrier

Bernardo D’Auria and Alessandro Ferriero
Additional contact information
Bernardo D’Auria: Department of Statistics, Madrid University Carlos III (UC3M), Avenida de la Universidad 30, 28911 Leganés (Madrid), Spain
Alessandro Ferriero: Department of Mathematics, The Autonomous University of Madrid (UAM), Campus de Cantoblanco, 28049 Madrid, Spain

Mathematics, 2020, vol. 8, issue 1, 1-14

Abstract: In this paper, we study the optimal stopping-time problems related to a class of Itô diffusions, modeling for example an investment gain, for which the terminal value is a priori known. This could be the case of an insider trading or of the pinning at expiration of stock options. We give the explicit solution to these optimization problems and in particular we provide a class of processes whose optimal barrier has the same form as the one of the Brownian bridge. These processes may be a possible alternative to the Brownian bridge in practice as they could better model real applications. Moreover, we discuss the existence of a process with a prescribed curve as optimal barrier, for any given (decreasing) curve. This gives a modeling approach for the optimal liquidation time, i.e., the optimal time at which the investor should liquidate a position to maximize the gain.

Keywords: Hamilton–Jacobi–Bellman equation; optimal stopping time; Brownian bridge; liquidation strategy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/1/123/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/1/123/ (text/html)

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:gam:jmathe:v:8:y:2020:i:1:p:123-:d:308454

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().