Evolution of Shares in a Proof-of-Stake Cryptocurrency

Management Science, Volume 67, February 2021, Pages 661-672 (Lead Article)

HEC Paris Research Paper No. FIN-2019-1339

31 Pages Posted: 20 May 2019 Last revised: 1 Mar 2021

See all articles by Ioanid Rosu

Ioanid Rosu

HEC Paris - Finance Department

Fahad Saleh

Wake Forest University - Schools of Business

Date Written: July 30, 2020

Abstract

Do the rich always get richer by investing in a cryptocurrency for which new coins are issued according to a Proof-of-Stake (PoS) protocol? We answer this question in the negative: Without trading, the investor shares in the cryptocurrency are martingales that converge to a well-defined limiting distribution, hence are stable in the long run. This result is robust to allowing trading when investors are risk-neutral. Then, investors have no incentive to accumulate coins and gamble on the PoS protocol, but weakly prefer not to trade.

Keywords: Blockchain, cryptocurrency, asset allocation, martingale, Polya urn, Dirichlet distribution

JEL Classification: C6, G11

Suggested Citation

Rosu, Ioanid and Saleh, Fahad, Evolution of Shares in a Proof-of-Stake Cryptocurrency (July 30, 2020). Management Science, Volume 67, February 2021, Pages 661-672 (Lead Article), HEC Paris Research Paper No. FIN-2019-1339, Available at SSRN: https://ssrn.com/abstract=3377136 or http://dx.doi.org/10.2139/ssrn.3377136

Ioanid Rosu (Contact Author)

HEC Paris - Finance Department ( email )

1 rue de la Liberation
Jouy-en-Josas Cedex, 78351
France

Fahad Saleh

Wake Forest University - Schools of Business

P.O. Box 7659
Winston-Salem, NC 27109-7285
United States

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