As smart contract platforms autonomously manage billions of dollars of capital, quantifying the portfolio risk that investors engender in these systems is increasingly important. Recent work illustrates that Proof of Stake (PoS) is vulnerable to financial attacks arising from on-chain lending and has worse capital efficiency than Proof of Work (PoW) \cite{fanti_pos_econ}. Numerous methods for improving capital efficiency have been proposed that allow stakers to create fungible derivative claims on their staked assets. In this paper, we construct a unifying model for studying the security risks of these proposals. This model combines birth-death P\'olya processes and risk models adapted from the credit derivatives literature to assess token inequality and return profiles. We find that there is a sharp transition between 'safe' and 'unsafe' derivative usage. Surprisingly, we find that contrary to \cite{fanti2019compounding} there exist conditions where derivatives can \emph{reduce} concentration of wealth in these networks. This model also applies to Decentralized Finance (DeFi) protocols where staked assets are used as insurance. Our theoretical results are validated using agent-based simulation.

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可以借款时为什么要质押？

随着智能合约平台自主管理数十亿美元的资本，量化投资者在这些系统中产生的投资组合风险变得越来越重要。最近的工作表明，权益证明 (PoS) 容易受到链上借贷引起的金融攻击，并且资本效率比工作证明 (PoW) \cite{fanti_pos_econ} 差。已经提出了许多提高资本效率的方法，这些方法允许抵押者对其抵押资产创建可替代的衍生债权。在本文中，我们构建了一个统一模型来研究这些提议的安全风险。该模型结合了生死 P\'olya 过程和改编自信用衍生品文献的风险模型，以评估代币不平等和回报状况。我们发现“安全”和“ 不安全的衍生用法。令人惊讶的是，我们发现与 \cite{fanti2019compounding} 相反，存在衍生品可以\emph {减少}这些网络中财富的集中度的条件。该模型也适用于将抵押资产用作保险的去中心化金融 (DeFi) 协议。我们的理论结果使用基于代理的模拟进行了验证。