On the existence of personal equilibria

ArXiv ID: 2512.08348 “View on arXiv”

Authors: Laurence Carassus, Miklós Rásonyi

Abstract

We consider an investor who, while maximizing his/her expected utility, also compares the outcome to a reference entity. We recall the notion of personal equilibrium and show that, in a multistep, generically incomplete financial market model such an equilibrium indeed exists, under appropriate technical assumptions.

Keywords: Personal Equilibrium, Utility Maximization, Incomplete Market, Reference Dependence, Game Theory, General/Asset Pricing

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is heavily mathematical, using advanced tools like Schauder’s fixed point theorem and Hölder continuity proofs in Banach spaces, but it focuses purely on theoretical existence under abstract assumptions with no data, backtests, or implementation details.

  flowchart TD
    A["Research Goal:<br>Existence of Personal Equilibrium<br>in Incomplete Markets"] --> B["Methodology:<br>Game Theory Framework<br>Utility Maximization"]
    B --> C["Model Setup:<br>Multi-step Incomplete Market<br>Reference Dependence"]
    C --> D["Key Assumption:<br>Technical Conditions<br>e.g., Market Structure"]
    D --> E["Computational Process:<br>Fixed Point Argument<br>Existence Proof"]
    E --> F["Key Findings:<br>Equilibrium Exists<br>for General Incomplete Markets"]
    F --> G["Outcome:<br>Validates Reference-Dependent<br>Utility Models"]