On Risk-Sensitive Decision Making Under Uncertainty

ArXiv ID: 2404.13371 “View on arXiv”

Authors: Unknown

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.

Keywords: Stochastic Control, Dynamic Programming, Risk-Sensitive Optimization, Bellman Equation, Inventory Management, General Financial Markets

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper is mathematically dense, featuring stochastic control formulations, KKT conditions, and non-convex optimization, but it lacks empirical testing, backtests, or implementation-heavy details, offering only theoretical illustrations.

  flowchart TD
    A["Research Goal:<br>Risk-Sensitive Decision Making Under Uncertainty"] --> B["Formulate Stochastic Control Problem"]
    B --> C{"Key Methodology:<br>Dynamic Programming & Bellman Equation"}
    C --> D["Data/Inputs:<br>Deterministic & Stochastic Alternatives"]
    D --> E["Computational Process:<br>Necessary Optimality Conditions"]
    E --> F["Outcomes:<br>General Theory & Optimal Policies"]
    F --> G["Validation:<br>Examples in Inventory Management & Optimal Betting"]