Paper: arXiv 2312.14437

Authors: Zongxia Liang, Keyu Zhang

Abstract

In this paper we study a time-inconsistent portfolio optimization problem for competitive agents with CARA utilities and non-exponential discounting. The utility of each agent depends on her own wealth and consumption as well as the relative wealth and consumption to her competitors. Due to the presence of a non-exponential discount factor, each agent’s optimal strategy becomes time-inconsistent. In order to resolve time-inconsistency, each agent makes a decision in a sophisticated way, choosing open-loop equilibrium strategy in response to the strategies of all the other agents. We construct explicit solutions for the $n$-agent games and the corresponding mean field games (MFGs) where the limit of former yields the latter. This solution is unique in a special class of equilibria.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a rigorous theoretical analysis of open-loop equilibrium strategies in time-inconsistent n-agent and mean field games with non-exponential discounting. While the mathematical derivation of explicit solutions is highly complex and novel, the paper is purely theoretical and completely lacks empirical validation or real-world data application.

Research Flowchart

  flowchart TD
    A[Research Goal: Resolve Time-Inconsistent Portfolio Games with Relative Performance & Non-Exponential Discounting] --> B[Inputs: CARA Utilities, Multi-Asset Market, Non-Exponential Discount Factors]
    
    B --> C[Methodology: Formulate Open-Loop Equilibrium for Time-Inconsistent n-Agent Game]
    
    C --> D[Computational Process: Construct Explicit n-Agent Solutions & Pass to Limit]
    
    D --> E[Mean Field Game MFG: Derive Limit MFG Strategy from n-Agent Equilibrium]
    
    E --> F[Key Outcomes: Unique Explicit Open-Loop Equilibrium & Rigorous n-Agent to MFG Convergence]

Cited References (35)

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0 of 35 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.