We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton–Jacobi–Bellman equation usually calls for strong assumptions on the dynamics of the processes involved and the set of constraints. To treat this problem in the absence of those assumptions, we first convert it into a state-constrained stochastic target problem and then solve the latter by a level-set approach. With this approach, state constraints are managed through an exact penalization technique.

中文翻译：

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控制损失约束下随机最优控制问题的水平集方法

我们研究了一组在不同确定性日期保持的受控损失约束下的一系列最优控制问题。用 Hamilton-Jacobi-Bellman 方程表征相关价值函数通常需要对所涉及过程的动力学和约束集进行强有力的假设。为了在没有这些假设的情况下处理这个问题，我们首先将其转换为状态约束的随机目标问题，然后通过水平集方法解决后者。使用这种方法，状态约束通过精确惩罚技术进行管理。