Paper: arXiv 2410.19030

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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).

Research Flowchart

  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"]

Cited References (8)

  1. Understanding Ramsey-de Finetti Probabilities and the St. Petersburg Paradox (2023) — link
  2. Decision Making Under Uncertainty (2014) — link
  3. Decision Making Under Uncertainty: The Case of State-Dependent Preferences. (1986) — link
  4. Ambiguity Aversion and Comparative Ignorance (1995)
  5. Maxmin Expected Utility with Non-Unique Prior (1989) — link
  6. Loss Aversion and State-Dependent Linear Utility Functions
  7. (2023a) Understanding Expected Utility for Decision Making
  8. (a) If (x, p)  MSP (x, q) then [Eu(x, p) > Eu(x, q) for all linear utility profile u which is increasing-concave with respect to x]

0 of 8 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.