Classifying Financial Markets up to Isomorphism: Classifying Markets up to Isomorphism

TY - JOUR

T1 - Classifying Financial Markets up to Isomorphism

T2 - Classifying Markets up to Isomorphism

AU - Armstrong, John

PY - 2020/9/2

Y1 - 2020/9/2

N2 - Two markets should be considered isomorphic if they are financially indistinguishable. We define a notion of isomorphism for financial markets in both discrete and continuous time. We then seek to identify the distinct isomorphism classes, that is to classify markets.We classify complete one-period markets. We define an invariant of continuous time complete markets which we call the absolute market price of risk. This invariant plays a role analogous to the curvature in Riemannian geometry. We classify markets when the absolute market price of risk is deterministic.We show that, in general, markets with non-trivial automorphism groups admit mutual fund theorems. We prove a number of such theorems.

AB - Two markets should be considered isomorphic if they are financially indistinguishable. We define a notion of isomorphism for financial markets in both discrete and continuous time. We then seek to identify the distinct isomorphism classes, that is to classify markets.We classify complete one-period markets. We define an invariant of continuous time complete markets which we call the absolute market price of risk. This invariant plays a role analogous to the curvature in Riemannian geometry. We classify markets when the absolute market price of risk is deterministic.We show that, in general, markets with non-trivial automorphism groups admit mutual fund theorems. We prove a number of such theorems.

KW - category theory

KW - financial market

KW - isomorphism

KW - mutual fund theorem

UR - http://www.scopus.com/inward/record.url?scp=85093107109&partnerID=8YFLogxK

U2 - 10.1098/rspa.2020.0264

DO - 10.1098/rspa.2020.0264

M3 - Article

SN - 1364-5021

VL - 476

JO - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences

JF - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences

IS - 2241

M1 - 20200264

ER -