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On Risk-Sensitive Decision Making Under Uncertainty
Published 20 Apr 2024 in math.OC, cs.SY, eess.SY, q-fin.CP, and stat.ME | (2404.13371v1)
Abstract: 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.
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