Criteria for the absence of arbitrage in general diffusion markets

Paper: arXiv 2306.11470

Authors: David Criens, Mikhail Urusov

Abstract

We establish deterministic necessary and sufficient conditions for the no-arbitrage notions NA (“no arbitrage”), NUPBR (“no unbounded profit with bounded risk”) and NFLVR (“no free lunch with vanishing risk”) in general diffusion market models with finite and infinite time horizons. These are single asset models whose (discounted) asset price process $Y$ is a regular continuous strong Markov process that is also a semimartingale. We further characterize the existence of an equivalent martingale measure in such models. All deterministic criteria are provided in terms of the scale function and the speed measure of $Y$.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents deep, rigorous theoretical results regarding classical no-arbitrage conditions (NA, NUPBR, NFLVR) in continuous-time Markovian diffusion markets using advanced stochastic calculus. However, as a purely theoretical paper, it lacks empirical validation, empirical data, or code implementation.

Research Flowchart

  flowchart TD
    A["Research Goal: Establish deterministic criteria for no-arbitrage notions (NA, NUPBR, NFLVR) in diffusion markets"] --> B["Input: Discounted asset price process Y<br>(Regular continuous strong Markov semimartingale)"]
    B --> C["Compute Scale Function & Speed Measure of Y"]
    C --> D["Analyze Boundary Behavior & Integrability Properties"]
    D --> E["Formulate Necessary & Sufficient Conditions"]
    E --> F["Outcomes: Characterized NA, NUPBR, NFLVR, and EMM existence via deterministic criteria"]