In the Decentralized Finance (DeFi) setting, we present a new parametrized family of Constant Function Market Makers (CFMMs) which we call the Generalized Mean Market Makers (G3Ms), based on the generalized means. The G3Ms are intermediate between the Arithmetic Mean and Geometric Mean CFMM models, which G3Ms incorporate as special cases. We also present an extension of the G3Ms, based on the so-called Generalized f-Means, called Generalized f-Mean Market Makers (Gf3Ms). We show in addition that the G3Ms possess certain properties preferable to those exhibited by either the Arithmetic Mean CFMM or the Geometric Mean CFMM alone.
Alyssa Blackburn, Christoph Huber, Yossi Eliaz, Muhammad Shahzads Shamim · 9 authors
Bitcoin is a digital currency designed to rely on a decentralized, trustless network of anonymous agents. Using a pseudonymous-address-linking procedure that achieves >99% sensitivity and >99% specificity, we reveal that between launch (January 3rd, 2009), and when the price reached $1 (February 9th, 2011), most bitcoin was mined by only sixty-four agents. This was due to the rapid emergence of Pareto distributions in bitcoin income, producing such extensive resource centralization that almost all contemporary bitcoin addresses can be connected to these top agents by a chain of six transactions. Centralization created a social dilemma. Attackers could routinely exploit bitcoin via a "51% attack", making it possible for them to repeatedly spend the same bitcoins. Yet doing so would harm the community. Strikingly, we find that potential attackers always chose to cooperate instead. We model this dilemma using an N-player Centipede game in which anonymous players can choose to exploit, and thereby undermine, an appreciating good. Combining theory and economic experiments, we show that, even when individual payoffs are unchanged, cooperation is more frequent when the game is played by an anonymous group. Although bitcoin was designed to rely on a decentralized, trustless network of anonymous agents, its early success rested instead on cooperation among a small group of altruistic founders.
In the paper we investigate consensus formation, from an economic perspective, in a Proof-of-Stake (PoS) based platform inspired by the Algorand blockchain. In particular, we consider PoS in relation to governance, focusing on two main issues. First we discuss alternative sampling schemes, which can be adopted to select voting committees and to define the number of votes of committee members. The selection probability is proportional to one’s stake and increases with it. Participation in governance allows users to affect the platform’s decisions as well as to obtain a reward. Then, based on such preliminary analysis, we introduce a microeconomic model to investigate the optimal stake size for a generic user. In the model we conceptualize an optimal stake, for a user, as striking the balance between having Algos immediately available for transactions and setting aside currency units to increase the probability of becoming a committee member. Our main findings suggest that the optimal stake can be quite sensitive to the user’s preferences and to the rules for selecting committees. We believe the findings may support policy decisions in PoS based platforms.
The paper highlights some commonalities between the development of cryptocurrencies and the evolution of ecosystems. Concepts from evolutionary finance embedded in toy models consistent with stylized facts are employed to understand what survival of the fittest means in cryptofinance. Stylized facts for ownership, trading volume and market capitalization of cryptocurrencies are selectively presented in terms of scaling laws.
In this chapter structures that generate yield in cryptofinance will be analyzed and related to leverage. While the majority of crypto-assets do not have intrinsic yields in and of themselves, similar to cash holdings of fiat currency, revolutionary innovation based on smart contracts, which enable decentralised finance, does generate return. Examples include lending or providing liquidity to an automated market maker on a decentralised exchange, as well as performing block formation in a proof of stake blockchain. On centralised exchanges, perpetual and finite duration futures can trade at a premium or discount to the spot market for extended periods with one side of the transaction earning a yield. Disparities in yield exist between products and venues as a result of market segmentation and risk profile differences. Cryptofinance was initially shunned by legacy finance and developed independently. This led to curious and imaginative adaptions, reminiscent of Darwin's finches, including stable coins for dollar transfers, perpetuals for leverage, and a new class of exchanges for trading and investment.
We leverage a transaction costs narrative to provide a theoretically unified presentation of the evolution of exchange, with the latest evolutionary frontier being cryptocurrency and decentralized finance. We show that with each new development in the evolution of money, the new form or medium of exchange must reduce transaction costs relative to relevant alternatives. The development of blockchain and cryptocurrency reduced the cost of transferring currency by removing the need for a trusted third party to intermediate funds while also providing the benefit of anonymity/pseudonymity. Likewise, decentralized finance does not require a third party to intermediate savings and investment and can provide contingent anonymity to borrowers. While these innovations have attracted investment in the economically developed world, they appear to have significantly reduced transaction costs for transactors who might otherwise be defrauded of funds by corrupt governments who may extort third parties responsible for intermediating funds.
We review the recent developments in dynamic inventory models with financial flow considerations. The focus is on the literature that introduces cash flow dynamics into the classic inventory models that do not explicitly consider the interactions between physical (or material) and financial flows. These augmented models serve two important purposes. First, they help understand the impact of financial flows on inventory dynamics and decisions. Second, with the connection to the classic inventory models, one can leverage the extant results to derive the optimal control policy or to evaluate/optimize the performance of any given type of policy and reveal insights. We summarize models for both single-stage and multi-stage inventory systems, and discuss the implications and applications to decentralized systems within a broader topic of supply chain finance.
Bit coin might be known as the first crypto currency, the truth holds that it has been the first successful attempt towards the path of decentralized world that paved the way for vast technological advances bring forth thousands of coins in the new online world.Based on respective block chains and operated as a peer-to-peer network, its security is guaranteed by cryptographic algorithms instead of the sovereigns of the respective countries and has the potential to become a major means of payment for ecommerce, trading and as it forays into the art world who knows what the future of block chain holds.Instead of serving one country or some countries, block chain serves the entire world.
Ludwig von Mises produced an impossibility theorem indicating that economic calculation in the absence of market prices was impossible. This gave rise to the ‘socialist calculation debate’ in the first half of the twentieth century. This paper makes use of the insights of that debate to shed light on other situations where decision makers are required to allocate resources in areas where there are no market prices. A pertinent example would be most corporate social responsibility programs. In the absence of market prices local information cannot be communicated to decision makers. The paper further argues that blockchain technology can create the institutional environment for markets to emerge and consequently overcome the problem of missing prices.
We examine the distribution of realized Bitcoin daily log-returns and find significantly-thin tails. From there we construct a simple connection back to traditional volatility modelling. And then we discuss how this connection can serve as a foundation to leverage existing derivative quant research to explore cryptocurrency market dynamics. These results also suggest a connection between cryptocurrency exchange structure and trading dynamics.
Optimal simple rules for the monetary policy of the first stochastically dominant crypto-currency are derived in a Dynamic Stochastic General Equilibrium (DSGE) model, in order to provide optimal responses to changes in inflation, output, and other sources of uncertainty. The optimal monetary policy stochastically dominates all the previous crypto-currencies, thus the efficient portfolio is to go long on the stochastically dominant crypto-currency: a strategy-proof arbitrage featuring a higher Omega ratio with higher expected returns, inducing an investment-efficient Nash equilibrium over the crypto-market. Zero-knowledge proofs of the monetary policy are committed on the blockchain: an implementation is provided.
Potreba izdavanja maloprodajnog digitalnog novca od strane središnjih banaka za građanstvo sve se češće spominje kao nužnost, ponajprije zbog financijske inkluzije i smanjenja korištenja gotovine u proteklih nekoliko godina. Osim toga, središnje banke razmatraju korištenje tehnologije raspodijeljenih glavnih knjiga zbog ubrzavanja veleprodajnog plaćanja i trgovanja imovinom te izbjegavanja korištenja pružatelja usluga u tu svrhu. S tim u vidu niz središnjih banaka u svijetu u posljednjih nekoliko godina pokrenuo je projekte i pilote za testiranje DLT sustava u svrhu izdavanja, trgovanja i plaćanja CDBC-om. Ovaj rad donosi načine provedbe i zaključke iz najznačajnijih te najbolje dokumentiranih istraživanja i pilota provedenih u tu svrhu. Nakon toga, rad ukratko prolazi kroz specifičnosti najčešće korištenih DLT platformi u navedenim istraživanjima i pilotima. Naposljetku se rad bavi sigurnosnim aspektima izdavanja CDBC-a na DLT platformi, uključujući tehnike za unaprjeđenje povjerljivosti te moguće ranjivosti i programske greške pametnih ugovora, te najboljim praksama koje bi trebalo slijediti kako bi se osigurala sigurnost takvih sustava.
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.
The benefits offered by cryptocurrencies are a great many: transaction cost and speed, security and transparency, to name a few. Yet, there is also a major drawback represented by their extremely high volatility. Stablecoins offer an ideal solution since they preserve all the advantages of blockchain-based currencies, while reducing considerably the volatility issue. Currently, stablecoins are almost exclusively pegged to the US Dollar and secured by non-crypto assets held in account at custodial institutions. In this article, we present the design of a decentralized organization aimed at issuing stablecoins backed by crypto-assets stored on-chain and pegged to assets different from fiat money. Our model offers several advantages, in particular, it allows the issuance of stablecoins in a trustless, permission-less and non-custodial environment.
Decentralized Finance (DeFi) aims to use advancements in both computation and cryptography to tackle standard economic problems. It must, therefore, operate within the intersection of constraints required by both the computer science and economic domains. We explore a foundational question at the junction of those fields: is it possible to synthesize variable market-clearing risk-free yield for native tokens via smart contracts? We show using a stylized model representing a large class of existing decentralized consensus algorithms that this is not possible. This places strong bounds on what decentralized financial products can be built and constrains the shape of future developments in DeFi. Among other limitations, our results reveal that markets in DeFi are incomplete.
The financial crisis of 2007-08 revealed that centralized finance (CeFi) relying on large, interconnected financial institutions is easily destabilized. Since the crisis, significant regulatory tightening, monetary easing, and new competitors (e.g., fintechs) have created significant pressure on profit margins and CeFi business models. Recently, a new form of financial intermediation that functions independently of centralized intermediaries has emerged, namely decentralized finance (DeFi). DeFi relies on public, permissionless blockchains and uses so-called smart contracts to perform financial services such as borrowing, lending, and trading in a transparent and automated fashion. The paper gives an overview of DeFi and discusses its advantages and disadvantages compared to CeFi. We analyze different scenarios about the future paths of CeFi and DeFi, concluding that a convergence scenario is most likely.
Cryptocurrencies and decentralized finance (DeFi) are reshaping how value is created, exchanged, and governed, and this chapter positions them as more than speculative instruments by reading them as an emerging financial infrastructure. In an ideal digital economy, programmable money supports low-friction transactions, broad participation, and transparent rules, while users retain control without surrendering trust to dominant intermediaries. Yet that ideal remains unevenly realized: markets still absorb extreme volatility, smart contracts still fail under adversarial conditions, and regulatory responses still oscillate between accommodation and restriction, leaving innovation and consumer protection in tension. Prior scholarship has mapped the monetary properties of Bitcoin as a scarcity-driven “digital store of value,” and it has framed Ethereum as the computational base layer that makes smart contracts—and therefore DeFi—possible. Studies on decentralized exchanges, lending protocols, automated market makers, and liquidity incentives have shown how 328 intermediated functions can be replicated through code, but they have also documented exploit patterns, oracle manipulation, governance capture, and composability risks that propagate across protocols. What remains underdeveloped is an integrated account that connects asset design, protocol architecture, and institutional constraints into a single explanatory model. To address this gap, the study advances a sociotechnical framework that links blockchain trust primitives with financial intermediation theory. By tracing how cryptocurrencies supply liquidity and collateral to DeFi, while DeFi amplifies token utility and systemic exposure, the chapter clarifies the conditions under which decentralized finance can mature into a resilient, inclusive financial ecosystem.