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BSDEs driven by time-changed Lévy noises and optimal control

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  • Di Nunno, Giulia
  • Sjursen, Steffen

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.

Suggested Citation

  • Di Nunno, Giulia & Sjursen, Steffen, 2014. "BSDEs driven by time-changed Lévy noises and optimal control," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1679-1709.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:4:p:1679-1709
    DOI: 10.1016/j.spa.2013.12.010
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    1. Wu, Hao & Li, Xuefeng, 2021. "Converse comparison theorems for multidimensional anticipated backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 168(C).

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