Enlargement of Filtrations: An Exposition of Core Ideas with Financial Examples

Paper: arXiv 2303.03573

Authors: Karen Grigorian, Robert A. Jarrow

Abstract

In this paper we provide an exhaustive survey of the current state of the mathematics of filtration enlargement and an interpretation of the key results of the literature from the viewpoint of mathematical finance. The emphasis is on providing a well-structured compendium of known mathematical results that can be used by researchers in mathematical finance. We mainly state the results and discuss their role and significance, with references provided for the omitted proofs. The discussion of mathematical results is accompanied by numerous examples from mathematical finance.

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 highly rigorous theoretical exposition of filtration enlargement mathematics applied to finance, featuring advanced stochastic calculus. However, as a pure mathematical survey and conceptual framework, it entirely lacks empirical backtesting and dataset validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Survey & Interpret Filtration Enlargement for Mathematical Finance] --> B[Core Theory: Semimartingale Theory & Stochastic Calculus]
    B --> C[Methodology: Compare Progressive vs Initial Enlargement]
    C --> D[Inputs: Financial Models of Information Asymmetry]
    D --> E[Analysis: Compute Drift Adjustments & Arbitrage Conditions]
    E --> F[Outcomes: Compendium of Mathematical Results & Multi-Asset Financial Applications]