IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2207.12581.html
   My bibliography  Save this paper

Trading under the Proof-of-Stake Protocol -- a Continuous-Time Control Approach

Author

Listed:
  • Wenpin Tang
  • David D. Yao

Abstract

We develop a continuous-time control approach to optimal trading in a Proof-of-Stake (PoS) blockchain, formulated as a consumption-investment problem that aims to strike the optimal balance between a participant's (or agent's) utility from holding/trading stakes and utility from consumption. We present solutions via dynamic programming and the Hamilton-Jacobi-Bellman (HJB) equations. When the utility functions are linear or convex, we derive close-form solutions and show that the bang-bang strategy is optimal (i.e., always buy or sell at full capacity). Furthermore, we bring out the explicit connection between the rate of return in trading/holding stakes and the participant's risk-adjusted valuation of the stakes. In particular, we show when a participant is risk-neutral or risk-seeking, corresponding to the risk-adjusted valuation being a martingale or a sub-martingale, the optimal strategy must be to either buy all the time, sell all the time, or first buy then sell, and with both buying and selling executed at full capacity. We also propose a risk-control version of the consumption-investment problem; and for a special case, the ''stake-parity'' problem, we show a mean-reverting strategy is optimal.

Suggested Citation

  • Wenpin Tang & David D. Yao, 2022. "Trading under the Proof-of-Stake Protocol -- a Continuous-Time Control Approach," Papers 2207.12581, arXiv.org, revised Jun 2023.
    • Handle: RePEc:arx:papers:2207.12581
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2207.12581
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jonathan Chiu & Thorsten V. Koeppl, 2017. "The Economics Of Cryptocurrencies - Bitcoin And Beyond," Working Paper 1389, Economics Department, Queen's University.
    2. Jiri Chod & Nikolaos Trichakis & Gerry Tsoukalas & Henry Aspegren & Mark Weber, 2020. "On the Financing Benefits of Supply Chain Transparency and Blockchain Adoption," Management Science, INFORMS, vol. 66(10), pages 4378-4396, October.
    3. Ioanid Roşu & Fahad Saleh, 2021. "Evolution of Shares in a Proof-of-Stake Cryptocurrency," Management Science, INFORMS, vol. 67(2), pages 661-672, February.
    4. Camilo Mora & Randi L. Rollins & Katie Taladay & Michael B. Kantar & Mason K. Chock & Mio Shimada & Erik C. Franklin, 2018. "Bitcoin emissions alone could push global warming above 2°C," Nature Climate Change, Nature, vol. 8(11), pages 931-933, November.
    5. Wenpin Tang & David D. Yao, 2022. "Polynomial Voting Rules," Papers 2206.10105, arXiv.org, revised Jan 2024.
    6. Charles Bertucci & Louis Bertucci & Jean-Michel Lasry & Pierre-Louis Lions, 2020. "Mean Field Game Approach to Bitcoin Mining," Papers 2004.08167, arXiv.org.
    7. Wenpin Tang, 2022. "Stability of shares in the Proof of Stake Protocol -- Concentration and Phase Transitions," Papers 2206.02227, arXiv.org.
    8. Chiu, Jonathan & Koeppl, Thorsten V, 2017. "The economics of cryptocurrencies – bitcoin and beyond," Working Paper Series 6688, Victoria University of Wellington, School of Economics and Finance.
    9. Fahad Saleh & Wei Jiang, 2021. "Blockchain without Waste: Proof-of-Stake [Proof of Work vs Proof of Stake]," The Review of Financial Studies, Society for Financial Studies, vol. 34(3), pages 1156-1190.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wenpin Tang & David D. Yao, 2023. "Transaction fee mechanism for Proof-of-Stake protocol," Papers 2308.13881, arXiv.org, revised Aug 2023.
    2. Wenpin Tang, 2023. "Trading and wealth evolution in the Proof of Stake protocol," Papers 2308.01803, arXiv.org, revised Aug 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wenpin Tang, 2023. "Trading and wealth evolution in the Proof of Stake protocol," Papers 2308.01803, arXiv.org, revised Aug 2023.
    2. Wenpin Tang, 2022. "Stability of shares in the Proof of Stake Protocol -- Concentration and Phase Transitions," Papers 2206.02227, arXiv.org.
    3. Julien Prat & Benjamin Walter, 2021. "An Equilibrium Model of the Market for Bitcoin Mining," Journal of Political Economy, University of Chicago Press, vol. 129(8), pages 2415-2452.
    4. Wenpin Tang & David D. Yao, 2023. "Transaction fee mechanism for Proof-of-Stake protocol," Papers 2308.13881, arXiv.org, revised Aug 2023.
    5. Hanna Halaburda & Guillaume Haeringer & Joshua Gans & Neil Gandal, 2022. "The Microeconomics of Cryptocurrencies," Journal of Economic Literature, American Economic Association, vol. 60(3), pages 971-1013, September.
    6. Parthajit Kayal & Purnima Rohilla, 2021. "Bitcoin in the economics and finance literature: a survey," SN Business & Economics, Springer, vol. 1(7), pages 1-21, July.
    7. Simplice A. Asongu & Nicholas M. Odhiambo, 2023. "Female unemployment, mobile money innovations and doing business by females," Journal of Innovation and Entrepreneurship, Springer, vol. 12(1), pages 1-26, December.
    8. Ke Wu & Spencer Wheatley & Didier Sornette, 2018. "Classification of cryptocurrency coins and tokens by the dynamics of their market capitalisations," Papers 1803.03088, arXiv.org, revised May 2018.
    9. Alexander Karaivanov, 2021. "Blockchains, Collateral and Financial Contracts," Discussion Papers dp21-03, Department of Economics, Simon Fraser University.
    10. Brunnermeier, Markus & Abadi, Joseph, 2018. "Blockchain Economics," CEPR Discussion Papers 13420, C.E.P.R. Discussion Papers.
    11. Bruno Biais & Christophe Bisière & Matthieu Bouvard & Catherine Casamatta & Albert J. Menkveld, 2023. "Equilibrium Bitcoin Pricing," Journal of Finance, American Finance Association, vol. 78(2), pages 967-1014, April.
    12. Saketh Aleti & Bruce Mizrach, 2021. "Bitcoin spot and futures market microstructure," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(2), pages 194-225, February.
    13. Charles M. Kahn & Francisco Rivadeneyra & Tsz-Nga Wong, 2020. "Eggs in One Basket: Security and Convenience of Digital Currencies," Working Papers 2020-032, Federal Reserve Bank of St. Louis.
    14. Jermann, Urban J., 2021. "Cryptocurrencies and Cagan’s model of hyperinflation," Journal of Macroeconomics, Elsevier, vol. 69(C).
    15. Asongu, Simplice A. & le Roux, Sara, 2023. "The role of mobile money innovations in transforming unemployed women to self-employed women in sub-Saharan Africa," Technological Forecasting and Social Change, Elsevier, vol. 191(C).
    16. Asongu, Simplice A. & Ngoungou, Yolande E. & Nnanna, Joseph, 2023. "Mobile money innovations and health performance in sub-Saharan Africa," Technology in Society, Elsevier, vol. 74(C).
    17. Silvia Bartolucci & Andrei Kirilenko, 2019. "A Model of the Optimal Selection of Crypto Assets," Papers 1906.09632, arXiv.org.
    18. Hosain, Md Sajjad, 2018. "Bitcoin: Future transaction currency?," MPRA Paper 87588, University Library of Munich, Germany.
    19. Li, Yiting & Wang, Chien-Chiang, 2019. "Cryptocurrency, Imperfect Information, and Fraud," MPRA Paper 94309, University Library of Munich, Germany.
    20. Zhanyi Jiao & Steven Kou & Yang Liu & Ruodu Wang, 2022. "An axiomatic theory for anonymized risk sharing," Papers 2208.07533, arXiv.org, revised May 2023.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2207.12581. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.