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

Research output: Contribution to journalArticle

Original languageEnglish
Article number20200264
JournalRoyal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
Issue number2241
Accepted/In press4 Aug 2020
Published2 Sep 2020


  • classifying_markets (12)

    classifying_markets_12_.pdf, 420 KB, application/pdf

    Uploaded date:04 Aug 2020

    Version:Accepted author manuscript

King's Authors


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.

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