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Evolution in pecunia
Journal article   Open access   Peer reviewed

Evolution in pecunia

Rabah Amir, Igor V. Evstigneev, Thorsten Hens, Valeriya Potapova and Klaus R. Schenk-Hoppé
Proceedings of the National Academy of Sciences - PNAS, Vol.118(26), e2016514118
06/29/2021
DOI: 10.1073/pnas.2016514118
PMCID: PMC8255991
PMID: 34172577
url
https://doi.org/10.1073/pnas.2016514118View
Published (Version of record) Open Access

Abstract

Significance We use an analogy between financial trading strategies and biological species and characterize an evolutionary stable strategy in an ecology with fix-mix strategies. The basis of our paper is that dividends are not exogenous but increase with the wealth invested in an asset, as is the case in a production economy. While this might create positive feedback loops, we show that the dynamical system has a unique evolutionary stable investment strategy that characterizes a locally stable equilibrium state. Our result is of high significance for any market economy since it shows that the dynamic interaction of investment strategies tends to produce stable prices. Mispricing therefore occurs only in extraordinary times when the market becomes highly dislocated due to exogenous events. The paper models evolution in pecunia—in the realm of finance. Financial markets are explored as evolving biological systems. Diverse investment strategies compete for the market capital invested in long-lived dividend-paying assets. Some strategies survive and some become extinct. The basis of our paper is that dividends are not exogenous but increase with the wealth invested in an asset, as is the case in a production economy. This might create a positive feedback loop in which more investment in some asset leads to higher dividends which in turn lead to higher investments. Nevertheless, we are able to identify a unique evolutionary stable investment strategy. The problem is studied in a framework combining stochastic dynamics and evolutionary game theory. The model proposed employs only objectively observable market data, in contrast with traditional settings relying upon unobservable investors’ characteristics (utilities and beliefs). Our method is analytical and based on mathematical reasoning. A numerical illustration of the main result is provided.

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