On Risk-Sensitive Decision Making Under Uncertainty

TL;DR

This paper formulates a risk-sensitive stochastic control problem for multi-stage decision-making under uncertainty, deriving optimality conditions and illustrating applications in betting and inventory management.

Contribution

It introduces a novel framework for risk-sensitive decision-making over multiple stages, with new optimality conditions and practical examples.

Findings

Derived necessary optimality conditions for the control problem.

Applied the theory to betting and inventory management scenarios.

Provided insights into risk-sensitive strategies under uncertainty.

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.