Market Viability and Completeness for Multinomial Models

Nahuel I. Arca

Papers from arXiv.org

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.

Date: 2025-08, Revised 2026-04
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