BSDEs driven by time-changed Lévy noises and optimal control

Giulia Di Nunno and Steffen Sjursen

Stochastic Processes and their Applications, 2014, vol. 124, issue 4, 1679-1709

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.

Keywords: BSDE; Time-change; Maximum principle; Doubly stochastic Poisson process; Conditionally independent increments (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2013.12.010

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