Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Jump-Filtration Consistent Nonlinear Expectations with $${\mathbb {L}^{p}}$$ L p Domains

Jump-Filtration Consistent Nonlinear Expectations with $${\mathbb {L}^{p}}$$ L p Domains Given $$p \in (1,2]$$ p ∈ ( 1 , 2 ] , the wellposedness of backward stochastic differential equations with jumps (BSDEJs) in $$\mathbb {L}^p$$ L p sense gives rise to a so-called g-expectation with $$\mathbb {L}^p$$ L p domain under the jump filtration (the one generated by a Brownian motion and a Poisson random measure). In this paper, we extend such a g-expectation to a nonlinear expectation $$\mathcal{E}$$ E with $$\mathbb {L}^p$$ L p domain that is consistent with the jump filtration. We study the basic (martingale) properties of the jump-filtration consistent nonlinear expectation $$\mathcal{E}$$ E and show that under certain domination condition, the nonlinear expectation $$\mathcal{E}$$ E can be represented by some g-expectation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Jump-Filtration Consistent Nonlinear Expectations with $${\mathbb {L}^{p}}$$ L p Domains

Applied Mathematics and Optimization , Volume 79 (1) – May 20, 2017

Loading next page...
 
/lp/springer-journals/jump-filtration-consistent-nonlinear-expectations-with-mathbb-l-p-l-p-EfdT0d28yV

References (53)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-017-9422-4
Publisher site
See Article on Publisher Site

Abstract

Given $$p \in (1,2]$$ p ∈ ( 1 , 2 ] , the wellposedness of backward stochastic differential equations with jumps (BSDEJs) in $$\mathbb {L}^p$$ L p sense gives rise to a so-called g-expectation with $$\mathbb {L}^p$$ L p domain under the jump filtration (the one generated by a Brownian motion and a Poisson random measure). In this paper, we extend such a g-expectation to a nonlinear expectation $$\mathcal{E}$$ E with $$\mathbb {L}^p$$ L p domain that is consistent with the jump filtration. We study the basic (martingale) properties of the jump-filtration consistent nonlinear expectation $$\mathcal{E}$$ E and show that under certain domination condition, the nonlinear expectation $$\mathcal{E}$$ E can be represented by some g-expectation.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: May 20, 2017

There are no references for this article.