Loss Aversion and State-Dependent Linear Utility Functions for Monetary Returns

ArXiv ID: 2410.19030 “View on arXiv”

Authors: Unknown

Abstract

We present a theory of expected utility with state-dependent linear utility functions for monetary returns, that incorporates the possibility of loss-aversion. Our results relate to first order stochastic dominance, mean-preserving spread, increasing-concave linear utility profiles and risk aversion. As an application of the expected utility theory developed here, we analyze the contract that a monopolist would offer in an insurance market that allowed for partial coverage of loss.

Keywords: Expected Utility Theory, Loss Aversion, Insurance Markets, Monopolist Contract, Stochastic Dominance, Insurance

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats
• Why: The paper develops a rigorous theoretical framework with stochastic dominance, mean-preserving spreads, and linear utility profiles, requiring advanced probability and utility theory; however, it lacks any data, backtests, or implementation details, relying solely on conceptual examples (e.g., a toy insurance model).

  flowchart TD
    A["Research Goal: Theory of Expected Utility<br>with State-Dependent Linear Utility<br>Incorporating Loss Aversion"] --> B["Methodology: Mathematical Modeling"]
    B --> C["Inputs: Assumptions on<br>Monetary Returns & Loss States"]
    C --> D{"Computational Processes"}
    D --> E["Derive State-Dependent<br>Linear Utility Functions"]
    D --> F["Analyze Stochastic Dominance<br>& Mean-Preserving Spreads"]
    D --> G["Compute Optimal Monopolist<br>Insurance Contract"]
    E & F & G --> H["Key Outcomes/Findings"]
    H --> I["Theoretical Framework for<br>Loss-Averse Expected Utility"]
    H --> J["Conditions for First-Order<br>Stochastic Dominance"]
    H --> K["Solution for Partial<br>Insurance Coverage"]