Paper: arXiv 2508.05022

Authors: Djibril Gueye, Alejandra Quintos

Abstract

We propose a multivariate framework for modeling dependent default times that extends the classical Cox process by incorporating both common and idiosyncratic shocks. Our construction uses càdlàg, increasing processes to model cumulative intensities, relaxing the requirement of absolutely continuous compensators. Analytical tractability is preserved through the multiplicative decomposition of Azéma supermartingales under assumptions that guarantee deterministic compensators. The framework captures a wide range of dependence structures and allows for both simultaneous and non-simultaneous defaults. We derive closed-form expressions for joint survival probabilities and illustrate the flexibility of the model through examples based on Lévy subordinators, compound Poisson processes, and shot-noise processes, encompassing several well-known models from the literature as special cases. Finally, we show how the framework can be extended to incorporate stochastic continuous components, thereby unifying gradual and abrupt sources of default risk.

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 extending multivariate Cox processes using filtration enlargement and Azéma supermartingale decompositions. However, it is purely theoretical without empirical backtesting, real data validation, or provided code implementation.

Research Flowchart

  flowchart TD
    A[Goal: Model Dependent Defaults via Multivariate Generalized Cox Process] --> B[Inputs: Common & Idiosyncratic Shocks via càdlàg Increasing Processes]
    B --> C[Methodology: Relax Absolute Continuity & Apply Azéma Supermartingale Decomposition]
    C --> D[Concrete Models: Lévy Subordinators, Compound Poisson & Shot-Noise Processes]
    D --> E[Extension: Incorporate Stochastic Continuous Components]
    E --> F[Outcomes: Closed-form Joint Survival Probabilities & Unified Risk Framework]

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0 of 50 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.