Paper: arXiv 2407.09321

Authors: Zaniar Ahmadi, Xiaowen Zhou

Abstract

For refracted skew Brownian motion (skew Brownian motion with two-valued drift), adopting a perturbation approach we find expressions of its potential densities. As applications, we recover its transition density and study its long-time asymptotic behaviors. In addition, we also compare with previous results on transition densities for skew Brownian motions. We propose two approaches for generating quasi-random samples by approximating the cumulative distribution function and discuss their risk measurement application.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides rigorous mathematical derivations for the potential measure and transition densities of Refracted Skew Brownian Motion using a perturbation approach. However, its empirical rigor is low as it focuses almost entirely on theoretical probability theory with only conceptual applications to risk measurement.

Research Flowchart

  flowchart TD
    A[Research Goal: Derive Potential Densities & Applications for Refracted Skew Brownian Motion] --> B[Methodology: Perturbation Approach]
    B --> C[Compute Potential Densities & Recover Transition Density]
    C --> D[Study Long-time Asymptotic Behaviors & Compare with Existing Models]
    C --> E[Generate Quasi-Random Samples via CDF Approximation]
    E --> F[Outcome: Application to Cross-Asset Quantitative Risk Measurement]

Cited References (38)

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and 30 more
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  2. On the constructions of the skew Brownian motion (2006)
  3. Temps locaux et equations differentielles stochastiques (1982)
  4. Density of skew Brownian motion and its functionals with application in finance (2017)
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  6. Multi-skewed Brownian motion and diffusion in layered media (2011)
  7. Skew Brownian motion and pricing European options (2007)
  8. A new closed-form formula for pricing European options under a skew Brownian motion (2018)
  9. Skew Ornstein–Uhlenbeck processes and their financial applications (2015)
  10. A simple trinomial lattice approach for the skew-extended CIR models (2017)
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0 of 38 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.