Paper: arXiv 2503.23221

Authors: Rolando Rubilar-Torrealba, Lisandro Fermin, Soledad Torres

Abstract

We propose to model the records of the maximum Drawdown in capital markets by means a Piecewise Deterministic Markov Process (PDMP). We derive statistical results such as the mean and variance that describes the sequence of maximum Drawdown records. In addition, we developed a simulation study and techniques for estimating the parameters governing the stochastic process, using a practical example in the capital market to illustrate the procedure.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical framework using Piecewise Deterministic Markov Processes (PDMP) and infinitesimal generators to model maximum drawdown records. However, based on the provided text, it focuses primarily on mathematical formulations and simulation design rather than exhaustive empirical backtesting on extensive market datasets.

Research Flowchart

  flowchart TD
    A[Goal: Model Maximum Drawdown Records in Capital Markets] --> B[Framework: Piecewise Deterministic Markov Process]
    B --> C[Data: Capital Market Equities Inputs]
    C --> D[Computational Pipeline: Parameter Estimation & Simulation]
    D --> E[Statistical Results: Derivation of Mean and Variance]
    D --> F[Practical Application: Capital Market Empirical Example]
    E & F --> G[Outcomes: Validated Stochastic Framework for Max Drawdown Records]

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  8. Portfolio sensitivity to changes in the maximum and the maximum drawdown (2010)
and 25 more
  1. Maximum drawdown (2004)
  2. Stochastic numerical methods for Piecewise Deterministic Markov Processes: applications in Neuroscience (2019)
  3. Piecewise deterministic Markov processes applied to fatigue crack growth modelling (2009)
  4. Do macroeconomic variables have regime-dependent effects on stock return dynamics? Evidence from the Markov regime switching model (2009)
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0 of 33 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.