BSDEs driven by time-changed Lévy noises and optimal control

Giulia Di Nunno; Steffen Sjursen

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arXiv · 1312.5120

BSDEs driven by time-changed Lévy noises and optimal control

Giulia Di Nunno·Steffen Sjursen

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Abstract

We study backward stochastic differential equations (BSDEs) for time-changed Lévy noises when the time-change is independent of the Lévy 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 Lévy noise. As an illustration we solve the mean-variance portfolio selection problem.

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BibTeX RIS

Giulia Di Nunno, Steffen Sjursen. 2013-12-18. BSDEs driven by time-changed Lévy noises and optimal control. https://arxiv.org/abs/1312.5120

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