Market Viability and Completeness for Multinomial Models

TL;DR

This paper investigates viability and completeness in finite markets, characterizes equivalent martingale measures, and explores limitations of discrete-time models in financial mathematics.

Contribution

It provides a convex combination characterization of martingale measures and an algorithm applicable to convex geometry problems, advancing market modeling theory.

Findings

Characterized the set of equivalent martingale measures as convex combinations.

Developed an algorithm for finding such measures.

Highlighted limitations of discrete-time models for continuous-time markets.

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.