%0 Unpublished work %T Evolution of Shares in a Proof-of-Stake Cryptocurrency %+ Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH) %A Rosu, Ioanid %A Saleh, Fahad %Z FIN-2019-1339 %8 2020-06-13 %D 2020 %R 10.2139/ssrn.3377136 %K Blockchain %K cryptocurrency %K asset allocation %K martingale %K Polya urn %K Dirichlet distribution %Z Humanities and Social Sciences/Business administrationPreprints, Working Papers, ... %X 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. %G English %Z HEC Research Paper Series %L hal-02896092 %U https://hec.hal.science/hal-02896092 %~ SHS %~ HEC %~ CNRS