skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Thursday, May 23 until 2:00 AM ET on Friday, May 24 due to maintenance. We apologize for the inconvenience.

Search for: All records

Award ID contains: 2206038

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. 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.

    more » « less
  2. Free, publicly-accessible full text available March 1, 2025
  3. We propose and study a new class of polynomial voting rules for a general decentralized decision/consensus system, and more specifically for the proof-of-stake protocol. The main idea, inspired by the Penrose square-root law and the more recent quadratic voting rule, is to differentiate a voter’s voting power and the voter’s share (fraction of the total in the system). We show that, whereas voter shares form a martingale process that converges to a Dirichlet distribution, their voting powers follow a supermartingale process that decays to zero over time. This prevents any voter from controlling the voting process and, thus, enhances security. For both limiting results, we also provide explicit rates of convergence. When the initial total volume of votes (or stakes) is large, we show a phase transition in share stability (or the lack thereof), corresponding to the voter’s initial share relative to the total. We also study the scenario in which trading (of votes/stakes) among the voters is allowed and quantify the level of risk sensitivity (or risk aversion) in three categories, corresponding to the voter’s utility being a supermartingale, a submartingale, and a martingale. For each category, we identify the voter’s best strategy in terms of participation and trading.

    Funding: W. Tang gratefully acknowledges financial support through the National Science Foundation [Grants DMS-2113779 and DMS-2206038] and through a start-up grant at Columbia University. D. D. Yao’s work is part of a Columbia–City University/Hong Kong collaborative project that is supported by InnoHK Initiative, the Government of Hong Kong Special Administrative Region, and the Laboratory for AI-Powered Financial Technologies.

    more » « less
    Free, publicly-accessible full text available February 7, 2025
  4. Free, publicly-accessible full text available February 1, 2025
  5. Free, publicly-accessible full text available January 1, 2025
  6. Free, publicly-accessible full text available January 1, 2025
  7. Free, publicly-accessible full text available December 1, 2024