Paper: arXiv 2609.35063

Authors: Jun Maeda

Abstract

We solve the perpetual liquidation problem for a geometric multi-skew Brownian motion carrying local-time pushes upward at a support level and downward at a resistance level, a model of technical analysis that is Markov in the price alone. Three geometries arise, separated by a closed-form criterion: the continuation band lies below resistance, straddles it, or pins its upper edge there. Selling into resistance is a conclusion rather than an assumption. Identification is asymmetric: exercise behaviour determines the support parameters exactly, while the strength of resistance is recoverable only on an interval with a closed-form endpoint.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly complex mathematical model for optimal liquidation, introducing novel dynamics with multi-skew Brownian motion. While theoretically strong, it lacks empirical validation or backtesting, placing it firmly in the ‘Lab Rats’ quadrant. The clarity is good for the target audience, but reproducibility is limited by the absence of code or data.

Research Flowchart

  flowchart TD
    A[Research Goal: Perpetual Liquidation with S&R Levels under Multi-Skew Brownian Motion] --> B(Methodology: Solve Perpetual Liquidation Problem);
    B --> C{Data/Inputs: Geometric Multi-Skew Brownian Motion, Support/Resistance Levels};
    C --> D(Computational Process: Derive Optimal Liquidation Strategy);
    D --> E{Outcomes: Three Geometries of Continuation Band};
    E --> F[Key Findings: Selling into Resistance, Asymmetric Identification of S&R Parameters];