Paper: arXiv 2410.16010

Authors: Bernardo D’Auria, Carlos Escudero

Abstract

We study the anticipating version of the classical portfolio optimization problem in a financial market with the presence of a trader who possesses privileged information about the future (insider information), but who is also subjected to a delay in the information flow about the market conditions; hence this trader possesses an asymmetric information with respect to the traditional one. We analyze it via the Russo-Vallois forward stochastic integral, i. e. using anticipating stochastic calculus, along with a white noise approach. We explicitly compute the optimal portfolios that maximize the expected logarithmic utility assuming different classical financial models: Black-Scholes-Merton, Heston, Vasicek. Similar results hold for other well-known models, such as the Hull-White and the Cox-Ingersoll-Ross ones. Our comparison between the performance of the traditional trader and the insider, although only asymmetrically informed, reveals that the privileged information overcompensates the delay in all cases, provided only one information flow is delayed. However, when two information flows are delayed, a competition between future information and delay magnitude enters into play, implying that the best performance depends on the parameter values. This, in turn, allows us to value future information in terms of time, and not only utility.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework combining Russo-Vallois forward stochastic integrals and white noise analysis to model portfolio optimization with delayed and privileged information. However, it is purely theoretical and entirely lacks empirical backtesting, real-world market data, or numerical simulations.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate portfolio performance for asymmetrically informed insider with delayed information] --> B[Financial Models Input: Black-Scholes-Merton, Heston, Vasicek]
    B --> C[Methodology: Anticipating Stochastic Calculus & Russo-Vallois Forward Integrals]
    C --> D[Optimization: Maximize Expected Logarithmic Utility for Delayed Insider vs. Traditional Trader]
    D --> E[Outcome 1: Single Delay - Privileged information overcompensates for information delay]
    D --> F[Outcome 2: Double Delay - Competition between future info & delay size dictates performance]
    E & F --> G[Key Conclusion: Quantified value of future information in terms of time]

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0 of 44 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.