Nonlinear Doob-Meyer decomposition with jumps.
type: Item
instance of: scholarly article
title: Nonlinear Doob-Meyer decomposition with jumps.
zbMATH Open document ID: 1048.91066
author: Qingquan Lin
publication date: 2003-01-01T00:00:00Z
review text: A nonlinear Doob-Meyer decomposition theorem and the smallest \(g\)-supersolution for the BSDE driven by Brownian motion are stated in work by \textit{S. Peng} [Probab. Theory Relat. Fields 113, No. 4, 473--499 (1999; Zbl 0953.60059)]. In this paper, the author considers the nonlinear Doob-Meyer decomposition theorem for the BSDE driven by both Brownian motion and the Poisson point process. To do this, the comparison theorem and the limit theorem of \(g\)-supersolution is discussed, and the concept of \(g\)-supermartingale is introduced. We note, that the limit theorem of \(g\)-supersolution began to be considered since the original work by \textit{N. El Karui} and \textit{M.-C. Quenez} [SIAM J. Control Optimization 33, 29--66 (1995; Zbl 0831.90010)].
reviewed by: Anatoliy Swishchuk
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 1921178
zbMATH Keywords: g-supermartingale
zbMATH Keywords: g-supersolution
zbMATH Keywords: Poisson process
MaRDI profile type: Publication
full work available at URL: s10114-002-0218-2
OpenAlex ID: W1983962060
cites work: Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market
cites work: Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type
cites work: Q3992729
cites work: On solutions of backward stochastic differential equations with jumps and applications
cites work: Q4274285
cites work: Backward stochastic differential equations with continuous coefficient
cites work: Stochastic Differential Utility
cites work: Smallest \(g\)-supersolution for BSDE with continuous drift coefficients
cites work: Adapted solutions of backward stochastic differential equations with non- Lipschitz coefficients
cites work: Necessary Conditions for Optimal Control of Stochastic Systems with Random Jumps
DOI: 10.1007/S10114-002-0218-2
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1921178