This paper studies a risk-sensitive decision-making problem under uncertainty. It considers a decision-making process that unfolds over a fixed number of stages, in which a decision-maker chooses among multiple alternatives, some of which are deterministic and others are stochastic. The decision-maker's cumulative value is updated at each stage, reflecting the outcomes of the chosen alternatives. After formulating this as a stochastic control problem, we delineate the necessary optimality conditions for it. Two illustrative examples from optimal betting and inventory management are provided to support our theory.

翻译：本文研究不确定性条件下的风险敏感型决策问题。考虑一个在固定阶段内展开的决策过程，决策者需从若干确定性与随机性并存的备选方案中做出选择。决策者的累积价值在每个阶段根据所选方案的结果进行更新。通过将该问题构建为随机控制模型，我们推导出其最优性必要条件。最后通过最优投注与库存管理两个示例验证了理论的有效性。