Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyers type
Download PDF
Download PDF
  • Published: March 1999

Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyers type

  • Shige Peng1 

Probability Theory and Related Fields volume 113, pages 473–499 (1999)Cite this article

  • 1012 Accesses

  • 199 Citations

  • Metrics details

Abstract

We have obtained the following limit theorem: if a sequence of RCLL supersolutions of a backward stochastic differential equations (BSDE) converges monotonically up to (y t ) with E[sup t |y t |2] < ∞, then (y t ) itself is a RCLL supersolution of the same BSDE (Theorem 2.4 and 3.6).

We apply this result to the following two problems: 1) nonlinear Doob–Meyer Decomposition Theorem. 2) the smallest supersolution of a BSDE with constraints on the solution (y, z). The constraints may be non convex with respect to (y, z) and may be only measurable with respect to the time variable t. this result may be applied to the pricing of hedging contingent claims with constrained portfolios and/or wealth processes.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Department of Mathematics, Shandong University, Jinan, 250100, P. R. China. e-mail: peng@public.jn.sd.cn and peng@sdu.edu.cn, , , , , , CN

    Shige Peng

Authors
  1. Shige Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 3 June 1997 / Revised version: 18 January 1998

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Peng, S. Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyers type. Probab Theory Relat Fields 113, 473–499 (1999). https://doi.org/10.1007/s004400050214

Download citation

  • Issue Date: March 1999

  • DOI: https://doi.org/10.1007/s004400050214

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • Mathematics Subject Classification (1991): 60H99, 60H30
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature