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The perturbation method applied to a robust optimization problem with constraint

Author

Listed:
  • Peng Luo

    (Shanghai Jiao Tong University)

  • Alexander Schied

    (University of Waterloo)

  • Xiaole Xue

    (Shandong University)

Abstract

The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the optimal solution using a terminal perturbation method and properties of Bounded Mean Oscillation (BMO) martingales. The necessary condition is further proved to be sufficient for the existence of an optimal solution under an additional convexity assumption. Finally, the optimality condition is applied to discuss problems of partial hedging with ambiguity, fundraising under ambiguity and randomized testing problems for a quadratic g-expectation.

Suggested Citation

  • Peng Luo & Alexander Schied & Xiaole Xue, 2024. "The perturbation method applied to a robust optimization problem with constraint," Mathematics and Financial Economics, Springer, volume 18, number 4, December.
    • Handle: RePEc:spr:mathfi:v:18:y:2024:i:1:d:10.1007_s11579-024-00358-y
    DOI: 10.1007/s11579-024-00358-y
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