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<p>In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for forward–backward control system under consistent convex expectation dominated by <i>G</i> -expectation. Under the smooth assumptions for the value function, we get the relationship between MP and DPP under a reference probability by establishing a useful estimate. If the value function is not smooth, then we obtain the first-order sub-jet and super-jet of the value function at any <i>t</i>. However, the processing method in this case is much more difficult than that when <i>t</i> equals 0.</p>

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Relationship Between Stochastic Maximum Principle and Dynamic Programming Principle Under Convex Expectation

  • 期刊论文

  • 发表日期：

    2025年7月22日

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  • Xiaojuan Li,
  • Mingshang Hu

摘要

In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for forward–backward control system under consistent convex expectation dominated by G -expectation. Under the smooth assumptions for the value function, we get the relationship between MP and DPP under a reference probability by establishing a useful estimate. If the value function is not smooth, then we obtain the first-order sub-jet and super-jet of the value function at any t. However, the processing method in this case is much more difficult than that when t equals 0.