Journal of Optimization Theory and Applications

, Volume 170, Issue 3, pp 1026–1054 | Cite as

Stochastic Perron for Stochastic Target Problems

  • Erhan Bayraktar
  • Jiaqi Li


In this paper, we adapt stochastic Perron’s method to analyze stochastic target problems in a jump diffusion setup, where the controls are unbounded. Since classical control problems can be analyzed under the framework of stochastic target problems (with unbounded controls), we use our results to generalize the results of Bayraktar and Sîrbu (SIAM J Control Optim 51(6):4274–4294, 2013) to problems with controlled jumps.


Stochastic target problems Stochastic Perron’s method Jump diffusion processes Viscosity solutions Unbounded controls 

Mathematics Subject Classification

93E20 49L20 49L25 60G46 



We would like to thank Bruno Bouchard who encouraged us to write this paper and for his constructive comments on its first version. We also thank the referees and the anonymous associate editor for their helpful comments, which helped us to improve our paper. This research is supported by the National Science Foundation under grant DMS-1613170.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.University of MichiganAnn ArborUSA

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