Evolution of Shares in a Proof-of-Stake Cryptocurrency

23 Pages Posted: 20 May 2019 Last revised: 25 Nov 2019

See all articles by Ioanid Rosu

Ioanid Rosu

HEC Paris - Finance Department

Fahad Saleh

McGill University - Desautels Faculty of Management

Date Written: November 22, 2019

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 Dirichlet 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 (November 22, 2019). 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

McGill University - Desautels Faculty of Management ( email )

1001 Sherbrooke St. West
Montreal, Quebec H3A1G5 H3A 2M1
Canada

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