Locally Lipschitz BSDE driven by a continuous martingale a path-derivative approach

Kihun Nam

Stochastic Processes and their Applications, 2021, vol. 141, issue C, 376-411

Abstract: Using a new notion of path-derivative, we study the well-posedness of backward stochastic differential equation driven by a continuous martingale M when f(s,γ,y,z) is locally Lipschitz in (y,z): Yt=ξ(M[0,T])+∫tTf(s,M[0,s],Ys−,Zsms)dtr[M,M]s−∫tTZsdMs−NT+Nt.Here, M[0,t] is the path of M from 0 to t and m is defined by [M,M]t=∫0tmsms∗dtr[M,M]s. When the BSDE is one-dimensional, we show the existence and uniqueness of the solution. On the contrary, when the BSDE is multidimensional, we show the existence and uniqueness only when [M,M]T is small enough: otherwise, we provide a counterexample. Then, we investigate the applications to optimal control of diffusion and optimal portfolio selection under various restrictions.

Keywords: Backward stochastic differential equation; Path differentiability; Functional derivative; Coefficients of superlinear growth; Utility maximization (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414921001514
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:141:y:2021:i:c:p:376-411

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.2021.09.009

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 ().