Paper: arXiv 2601.14139

Authors: Michail Anthropelos, Constantinos Kardaras, Constantinos Stefanakis

Abstract

In an incomplete financial market with general continuous semimartingale dynamics; we model an investor with log-utility preferences who, in addition to an initial capital, receives units of a non-traded endowment process. Using duality techniques, we derive the fourth-order expansion of the primal value function with respect to the units $ε$, held in the non-traded endowment. In turn, this lays the foundation for expanding the optimal wealth process, in this context, up to second order w.r.t. $ε$. The key processes underpinning the aforementioned results are given in terms of Kunita-Watanabe projections, mirroring the case of lower order expansions of similar nature. Both the case of finite and infinite horizons are treated in a unified manner.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous theoretical contribution by extending asymptotic expansions for log-utility maximization with non-traded endowments to the fourth order using continuous semimartingale theory and dual formulations. However, it is purely theoretical with no empirical backtests or market data analysis included in the text.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Log-Utility Investor with<br/>Small Non-Traded Endowment ε] --> B[Inputs: Continuous Semimartingales &<br/>Initial Capital + Small Liability Stream]
    B --> C[Methodology: Apply Duality Techniques &<br/>Kunita-Watanabe Projections]
    C --> D[Computation: Unified Finite/Infinite Horizon<br/>Asymptotic Expansions]
    D --> E[Outcome 1: 4th-Order Expansion of<br/>Primal Value Function w.r.t. ε]
    D --> F[Outcome 2: 2nd-Order Expansion of<br/>Optimal Wealth Process w.r.t. ε]

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2 of 87 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.