Paper: arXiv 2508.13966
Authors: Nahuel I. Arca
Abstract
In this paper we aim to study viability and completeness in finite markets. In order to do that, we characterize the set of equivalent martingale measures of two-period markets as convex combinations of a finite number of martingale measures. We provide an algorithm for finding such measures, that can be applied in other problems of convex geometry, and represents the starting point for a study of such characterizations of convex sets’ intersections. We apply these results to the study of a discrete-time version of the Korn-Kreer-Lenssen model, and give an example of the limitations of using discrete-time models to understand continuous-time ones.
Complexity vs Empirical Score
- Math Complexity: 7.5/10
- Empirical Rigor: 1.5/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper presents a rigorous theoretical exploration of equivalent martingale measures in discrete multinomial models using convex geometry and the Krein-Milman theorem. However, it is purely theoretical mathematical finance with no real-world market data, backtesting, or empirical validation.
Research Flowchart
flowchart TD
A[Research Goal: Characterize EMMs, Viability & Completeness in Finite Markets] --> B[Input: Two-Period Multinomial Market Model & Korn-Kreer-Lenssen Framework]
B --> C[Methodology: Convex Geometry & Set Intersections]
C --> D[Algorithm: Compute EMMs as Convex Combinations of Extremal Measures]
D --> E[Application: Discrete-Time Korn-Kreer-Lenssen Model Analysis]
E --> F[Findings: Characterization of EMMs & Limitations of Discrete Models for Continuous Time]