BSDEs driven by time-changed L\'evy noises and optimal control
Probability
2013-12-19 v1
Abstract
We study backward stochastic differential equations (BSDEs) for time-changed L\'evy noises when the time-change is independent of the L\'evy process. We prove existence and uniqueness of the solution and we obtain an explicit formula for linear BSDEs and a comparison principle. BSDEs naturally appear in control problems. Here we prove a sufficient maximum principle for a general optimal control problem of a system driven by a time-changed L\'evy noise. As an illustration we solve the mean-variance portfolio selection problem.
Cite
@article{arxiv.1312.5120,
title = {BSDEs driven by time-changed L\'evy noises and optimal control},
author = {Giulia Di Nunno and Steffen Sjursen},
journal= {arXiv preprint arXiv:1312.5120},
year = {2013}
}