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BSDEs driven by time-changed Lévy noises and optimal control

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.

preprint2013arXivOpen access
Giulia Di NunnoSteffen Sjursen
math.PR
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Open access2 authors1 topic
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Giulia Di NunnoSteffen Sjursen

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