Paper: arXiv 2311.04841

Authors: Gechun Liang, Moris S. Strub, Yuwei Wang

Abstract

We introduce predictable relative forward performance processes (PRFPP) as a new framework for studying portfolio management within a competitive and incomplete market environment. Each agent trades a distinct stock following a binomial distribution with probabilities for a positive return depending on the market regime characterized by a non-traded stochastic factor. For both the finite population and mean field games, we construct and analyse PRFPPs for initial data of the CARA class along with the associated equilibrium strategies. We find that relative performance concerns do not necessarily lead to more investment in the risky asset compared to when there are no such concerns. Under some parameter constellations, agents short a stock with positive expected excess return. The binomial market setting facilitates a straightforward adjustment of risky asset skewness, enabling an analysis of its impact on investment behavior, an aspect that continuous-time frameworks cannot capture.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a mathematically sophisticated framework extending forward performance processes to multi-agent and mean-field game settings with binomial markets. While mathematically rigorous and novel in its theoretical setup, it lacks empirical backtesting and real-world market data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Multi-Agent Portfolio Management via PRFPP in Incomplete Markets] --> B[Inputs: CARA Utility, Non-Traded Stochastic Factor, Binomial Asset Returns]
    B --> C[Formulate Finite Population & Mean Field Games]
    C --> D[Construct PRFPP & Derive Nash Equilibrium Strategies]
    D --> E[Analyze Skewness & Inter-Agent Competition Effects]
    E --> F[Outcomes: Relative concerns do not always boost risky investment; agents may short positive-return assets]

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1 of 83 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.