In the Delegated Proof-of-Stake blockchain, block producers (BP) are elected by stake-weighted vote. The supermajority of BPs can change the rule of the blockchain; thus, preventing the centralization of votes is important. We find the optimal number of votes per account (VPA) that minimizes takeover risks while maximizing voting flexibility. A smaller VPA requires more stake for takeover, but only up to a certain point, implying that the ‘one vote per account’ rule adopted by some major blockchains to mitigate centralization may be unnecessary. Our results are applicable to any environments in which multiple decision makers are elected by voting.
González, Agustín Muñoz, Juan I. Sequeira, Rafael Orive Illera
In this work, we present an application of the probabilistic weak formulation of mean field games (MFG) for modeling liquidity pools in a constant product automated market maker (AMM) protocol in the context of decentralized finance. Our work extends one of the most conventional applications of MFG, which is the price impact model in an order book, by incorporating an AMM instead of a traditional order book. The key structural difference is that in the AMM setting, the price is determined by the pool's reserves through a nonlinear mechanism, replacing the linear price-impact function used in classical models. Through our approach, we establish the existence of solutions to the Mean Field Game and, additionally, the existence of approximate Nash equilibria for the finite-player game. We complement the theoretical results with a comprehensive numerical study that validates the equilibrium structure: stability under perturbations, the $\varepsilon$-Nash property via unilateral deviations, finite-player convergence at propagation-of-chaos rates, and sensitivity to cost parameters and incentive targets. These results offer a new game-theoretic perspective for representing strategic behavior in AMM-based liquidity pools and open promising opportunities for future research in this emerging field.
Dmitry Kroo, Vladimir Gorgadze, George Ovchinnikov, Artem Barger
This paper introduces a novel quantitative framework for optimizing liquidity provider (LP) positions in decentralized finance (DeFi) markets, specifically focusing on Constant Product Market Makers (CPMMs). The proposed method constructs optimal mean-variance portfolios that are hedged by short positions in underlying tokens, thereby maximizing the Sharpe ratio. Unlike previous studies, which typically focus on single-pool strategies, our approach integrates multiple CPMM pools and accounts for transaction costs, offering a more comprehensive solution for risk management in DeFi. The model is rigorously tested on historical data from Uniswap V2, demonstrating significant outperformance over traditional liquidity provision strategies, with Sharpe ratios reaching up to 4. Additionally, the framework is shown to be scalable, maintaining positive returns even under high transaction costs and varying capital conditions. This work not only extends existing literature on DeFi liquidity provision but also provides a practical, implementable strategy for diversified portfolio management in volatile cryptocurrency markets.
Ken Huang, Youwei Yang, Fan Zhang, Xi Chen · 5 authors
Chapter 6 provides a comprehensive overview of tokenomics, analyzing the economic models and incentive mechanisms underlying tokens and cryptocurrencies. It explores the classification, functions, supply and demand dynamics, and financial aspects of various token types, including utility, governance, platform, stablecoins, NFTs, and meme coins. The interplay between tokenomics and Decentralized Finance (DeFi) is examined, highlighting considerations such as staking rewards and yields. Innovations such as "play to earn" gaming are covered but also their risks such as sustainability and Ponzi schemes. The impact of community sentiment and conviction on valuation is analyzed through meme coins and viral hype. Overall, this chapter offers crucial insights into the foundational economics of the Web3 ecosystem, grounded in a nuanced understanding of the incentive structures and value drivers behind diverse crypto tokens and assets. Both the technological potential and limitations are critically appraised. The key takeaway is an ability to comprehensively evaluate tokenomics across dimensions such as utility, supply, demand, distribution, financials, sentiment, and regulation.
The Bitcoin halving is a key event in the Bitcoin ecosystem that occurs approximately every four years or after all 210,000 blocks have been mined. This event is reduced to a double reward that miners receive for adding a new block to the blockchain, with the aim of controlling inflation and maintaining Bitcoin's deflationary model. This event helps to reduce the rate of issuance of new coins, which could theoretically lead to an increase in the price of Bitcoin, and to reduce the supply of constant or growing demand.
Today's article talks about the economic relations arising from the creation, accumulation, distribution and redistribution or use of centralized and decentralized monetary funds. Finance occurs in the monetary sector of the economy and is noted to occur on the basis of income
Options are fundamental to blockchain-based financial services, offering essential tools for risk management and price speculation, which enhance liquidity, flexibility, and market efficiency in decentralized finance (DeFi). Despite the growing interest in options for blockchain-resident assets, such as cryptocurrencies, current option mechanisms face significant challenges, including a high reliance on trusted third parties, limited asset support, high trading delays, and the requirement for option holders to provide upfront collateral. In this paper, we present a protocol that addresses the aforementioned issues. Our protocol is the first to eliminate the need for holders to post collateral when establishing options in trustless service environments (i.e. without a cross-chain bridge), which is achieved by introducing a guarantee from the option writer. Its universality allows for cross-chain options involving nearly \textit{any} assets on \textit{any} two different blockchains, provided the chains' programming languages can enforce and execute the necessary contract logic. Another key innovation is reducing option position transfer latency, which uses Double-Authentication-Preventing Signatures (DAPS). Our evaluation demonstrates that the proposed scheme reduces option transfer latency to less than half of that in existing methods. Rigorous security analysis proves that our protocol achieves secure option trading, even when facing adversarial behaviors.
Maria Grith, Caio Almeida, Ratmir Miftachov, Zijin Wang
We analyze the first and second moment risk premia in the Bitcoin market based on options and realized returns and contrast them to the premia embedded in the main US stock index market. First, Bitcoin is much more volatile and has a higher variance risk premium than the S&P 500. By decomposing the return premium into different regions of the return state space, we find that while most of the S&P 500 equity premium comes from mildly negative returns, the corresponding negative Bitcoin returns (between three and one standard deviations) account for only one-third of the total Bitcoin premium (BP). Further, applying a novel clustering algorithm to a collection of estimated Bitcoin option-implied risk-neutral densities, we find that risk premia vary over time as a function of two distinct market volatility regimes. The low-volatility regime implies a relatively high share of BP attributable to positive returns and a high Bitcoin Variance Risk Premium (BVRP). In high-volatility states, the BP attributable to positive and negative returns is more balanced, and the BVRP is lower. These results suggest Bitcoin investors are more concerned about variance and upside risk in a low-volatility regime.
Decentralized Finance (DeFi) has emerged as a transformative force in the financial sector, offering peer-to-peer financial services without traditional intermediaries such as banks. By utilizing blockchain technology and smart contracts, DeFi enables greater accessibility, transparency, and efficiency in financial transactions. However, the rapid expansion of DeFi poses significant challenges to global financial stability. This literature review explores the impact of DeFi on systemic risks, regulatory frameworks, and the traditional banking sector. While DeFi offers opportunities for financial inclusion and innovation, it also introduces new risks related to cybersecurity, liquidity, and market volatility. The absence of standardized regulations across jurisdictions exacerbates these risks, creating vulnerabilities in the global financial system. Furthermore, the interconnection between DeFi markets and traditional financial institutions increases the potential for spillover effects during periods of financial stress. This paper highlights the need for a balanced regulatory approach that fosters innovation while safeguarding financial stability. As DeFi continues to evolve, understanding its influence on global financial stability becomes increasingly important for policymakers, regulators, and financial institutions.
The article examines the essence of electronic money as an economic and legal phenomenon. The relevance of the introduction of innovative technologies in the financial development of modern society, which affect aspects of human life, has been determined. Blockchain technology is highlighted as one of the components of key innovations in the field of digital money. The impact of blockchain on the country’s payment system is substantiated. Blockchain functions are revealed, which open new horizons for the applications of technologies in various fields, making the world more efficient, safer and decentralized. Advantages and disadvantages of electronic money are defined and analyzed. The need to implement measures that would contribute to the mass spread of electronic money in Ukraine is substantiated. The prospects for the economy, which blockchain opens up for the development of decentralized business models, for changing the sphere of finance, are analyzed.Therefore, digital technologies are becoming a necessary cjmponent for the development of the modern economy and financial system. However, their implementation must take into account risks and ensure a high level of security and stability of the financial system. For example, the application of blockchain technologies can significantly simplify and ensure the security of financial transactions. It is also worth exploring the possibilities of using artificial intelligence and data analytics to improve financial decision-making. It is important to actively research and develop new technologies and approaches to ensure the safety and stability of the financial system in this new digital world.
Abstract. Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterize the continuous-time wealth dynamics of strategic liquidity providers (LPs) who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a self-financing and closed-form optimal liquidity provision strategy where the width of the LP’s liquidity range is determined by the profitability of the pool (provision fees minus gas fees), the predictable loss (PL) of the LP’s position, and concentration risk. Concentration risk refers to the decrease in fee revenue if the marginal exchange rate (akin to the midprice in a limit order book) in the pool exits the LP’s range of liquidity. When the drift in the marginal rate is stochastic, we show how to optimally skew the range of liquidity to increase fee revenue and profit from the expected changes in the marginal rate. Finally, we use Uniswap v3 data to show that, on average, LPs have traded at a significant loss, and to show that the out-of-sample performance of our strategy is superior to the historical performance of LPs in the pool we consider.
Decentralized lending is one of the key services in the field of decentralized finance. Due to its specifics, DeFi attracts participants all over the world, allowing you to fully take advantage of blockchain technologies. This article presents arguments emphasizing the key importance of interest rates in shaping the behavior of participants, allocating resources, and balancing supply and demand of financial products and services. The article also examines the impact of interest rates on the stability and efficiency of decentralized financial systems. In addition, it examines various approaches to setting interest rates in these ecosystems, including market mechanisms and algorithmic models.
Xinshu Dong, Orfeas Stefanos Thyfronitis Litos, Ertem Nusret Tas, David Tse · 7 authors
The idea of security sharing goes back to Nakamoto's introduction of merge mining, a technique that enables Bitcoin miners to reuse their hash power to bootstrap and secure other Proof-of-Work (PoW) blockchains. However, with the rise of Proof-of-Stake (PoS) chains, there is a need for new methods of Bitcoin security sharing. We introduce Bitcoin staking, a protocol that allows Bitcoin holders to trustlessly use their idle asset to secure a PoS chain. The key challenge is to enable automatic slashing of bitcoins on the Bitcoin chain upon safety violations on the PoS chain. We achieve this using double-authentication-preventing signatures, finality gadgets and bi-directional timestamping between Bitcoin and the PoS chain. Our design is entirely modular and can be integrated with any PoS chain. A version of this protocol was deployed to secure the Babylon mainnet in April 2025 and currently has over 58,000 bitcoins staked (about 4 billion USD at current prices) while paying only 0.05% APR reward to the stakers. This is 2 orders of magnitude cheaper security cost than in PoS chains secured by their native token.
분산 금융(DeFi)과 블록체인 기술의 결합은 금융 환경에서 획기적인 변화를 예고하며, 비교할 수 없는 투명성, 포괄성, 효율성을 약속한다. 그럼에도, 이 DeFi 분야는 주로 거래 비용 최적화와 다양한 이해 관계자의 인센티브 조정과 같은 중대한 도전에 직면하고 있다. 본 연구는 DeFi 풀이 내쉬 균형상태라는 새로운 검증 방식을 도입하여, DeFi 풀이 본질적으로 자체 규제하고 균형 상태를 유지할 수 있다는 가설을 검증하고자 한다. 수학적 표현과 시뮬레이션의 구현 방법을 통해, DeFi 프로토콜이 게임 이론의 원리를 활용할 수 있는 가능성을 밝혀내며, DeFi 생태계 내에서 프로토콜 설계의 안정성, 효율성, 공정성을 향상시키기 위한 방안을 제시한다.
Christoph Siebenbrunner, Alfred Taudes, Davor Svetinović
This paper examines the compatibility of full smart contracts with Central Bank Digital Currencies (CBDCs), emphasizing the constraints imposed by CBDCs' account limits and exploring this challenge through a requirements engineering lens. We analyze how these limits, essential for financial stability, inherently restrict the programmability of CBDCs, potentially limiting their utility in leveraging blockchain's full capabilities. By integrating a requirements analysis perspective, we offer a nuanced understanding of the system's needs, highlighting the trade-offs and implications for the design and functionality of CBDCs. This approach enriches the discourse by underscoring the importance of structured requirements practices in developing financially stable and technologically advanced CBDCs.
SHORT PAPER. This paper introduces the author’s current practical investigations, during the creation of a series of audio-visual installations and VR environments, ‘gamifying’ time-sequenced changes of multiple values, e.g., from financial data feeds. The work series critically reflect upon gambling tendencies in the global trading of various, increasingly immaterial assets. Algorithms and emotions of greed, euphoria, and despair meet in virtual scenery, where almost everything can be offered as a fungible and non-fungible token for exchange and trade. The project proposes speculative variations of dystopian “hybrid organisms” representing macroeconomic value exchange as a symbiotic relationship that competes for humanity’s attention and involvement.
Srisht Fateh Singh, Panagiotis Michalopoulos, Andreas Veneris
This paper investigates the current state of option trading platforms for cryptocurrencies, encompassing both centralized and decentralized exchanges. Option contracts in cryptocurrency markets offer functionalities akin to traditional markets, providing investors with tools to mitigate risks, particularly those arising from price volatility. The paper discusses these applications of option contracts in the context of decentralized finance, emphasizing their utility in managing market uncertainties. Despite a recent surge in the trading volume of option contracts on cryptocurrencies, decentralized platforms account for less than $1 \%$ of this total volume. Hence, this paper takes a closer look by examining the design choices of these platforms to understand the challenges hindering their growth and adoption. It identifies technical, financial, and adoption-related challenges faced by decentralized exchanges. Subsequently, the paper provides commentary on existing platform responses.
Mostafa Chegenizadeh, Shengnan Li, Claudio J. Tessone
In this paper, we conduct an in-depth analysis of the Cardano blockchain, focusing on the Proof of Stake (PoS) protocol, Ouroboros, and its implications for entity wealth and stake delegation dynamics within the ecosystem. Utilizing a heuristic-based address clustering method, previously introduced in the literature, we aggregate Cardano addresses to identify distinct entities within the network. This approach allows us to examine the wealth distribution and staking dynamics at an entity level, offering a unique perspective on the Cardano network’s economic behaviors. Our study reveals insightful patterns in the emergence of new entities and their participation in stake delegation, alongside the rewards they accrue. We investigate the distribution of wealth among these entities, employing statistical measures such as the probability density and the Gini index for wealth, delegated stakes, and rewards over the blockchain’s history. This analysis provides a comprehensive view of the wealth distribution within the Cardano ecosystem. Moreover, the paper explores how entities of varying wealth levels engage in stake delegation to pools of different sizes and the resultant reward distribution. We also delve into the temporal evolution of the number of pools within the network, examining how pools of various sizes are rewarded and the extent of inequality in reward distribution among them. Through this analysis, the paper sheds light on the complex interplay between wealth distribution, stake delegation, and reward mechanisms in the Cardano ecosystem, offering valuable insights into the economic and staking landscape of one of the leading blockchain networks.
Abstract. The purpose of a consensus protocol is to keep a distributed network of nodes “in sync,” even in the presence of an unpredictable communication network and adversarial behavior by some of the participating nodes. In the permissionless setting relevant to modern blockchain protocols, these nodes may be operated by a large number of unknown players, with each player free to use multiple identifiers and to start or stop running the protocol at any time. Establishing that a permissionless consensus protocol is “secure” thus requires both a distributed computing argument (that the protocol guarantees consistency and liveness unless the fraction of adversarial participation is sufficiently large) and an economic argument (that carrying out an attack would be prohibitively expensive for a potential attacker). There is a mature toolbox for assembling arguments of the former type; the goal of this paper is to lay the foundations for arguments of the latter type. For example, the Ethereum protocol is oft-claimed to be “more economically secure” after “the merge,” meaning in its current proof-of-stake incarnation relative to the (proof-of-work) original. What, formally, does this assertion mean? Is it true? Could there be alternative protocols that are “still more economically secure” than Ethereum? How do the answers depend on the assumptions imposed on, for example, the reliability of message delivery or the active participation of non-malicious players? An ideal permissionless consensus protocol would, in addition to satisfying standard consistency and liveness guarantees, render consistency violations prohibitively expensive for the attacker without collateral damage to honest participants—for example, by programatically confiscating an attacker’s resources without reducing the value of honest participants’ resources, as is the intention for slashing in a proof-of-stake protocol. We make this idea precise with our notion of the EAAC (expensive to attack in the absence of collapse) property and prove the following results: (1) In the synchronous and dynamically available setting (in which the communication network is reliable but nonmalicious players may be periodically inactive), with an adversary that controls at least one-half of the overall resources, no protocol can be EAAC. In particular, this result rules out EAAC for all typical longest-chain protocols (be they proof-of-work or proof-of-stake). (2) In the partially synchronous and quasi-permissionless setting (in which resource-controlling non-malicious players are always active but the communication network may suffer periods of unreliability), with an adversary that controls at least one-third of the overall resources, no protocol can be EAAC. In particular, slashing in a proof-of-stake protocol cannot achieve its intended purpose if message delays cannot be bounded a priori. (3) In the synchronous and quasi-permissionless setting, there is a proof-of-stake protocol with slashing that, provided the adversary controls less than two-thirds of the overall stake, satisfies the EAAC property. Thus, while only “classical security” is possible in the dynamically available or partially synchronous settings, proof-of-stake protocols with slashing can obtain additional “economic security” in the quasi-permissionless and synchronous settings. All three results are optimal with respect to the size of the adversary. With respect to Ethereum, our work formalizes the potential security benefits of proof-of-stake sybil-resistance coupled with slashing and the common belief that the merge has increased Ethereum’s economic security. Our work also provides mathematical justifications for several key design decisions behind the post-merge Ethereum protocol, ranging from long cooldown periods for unstaking to economic penalties for inactivity.
Exploring complex adaptive financial trading environments through multi-agent based simulation methods presents an innovative approach within the realm of quantitative finance. Despite the dominance of multi-agent reinforcement learning approaches in financial markets with observable data, there exists a set of systematically significant financial markets that pose challenges due to their partial or obscured data availability. We, therefore, devise a multi-agent simulation approach employing small-scale meta-heuristic methods. This approach aims to represent the opaque bilateral market for Australian government bond trading, capturing the bilateral nature of bank-to-bank trading, also referred to as "over-the-counter" (OTC) trading, and commonly occurring between "market makers". The uniqueness of the bilateral market, characterized by negotiated transactions and a limited number of agents, yields valuable insights for agent-based modelling and quantitative finance. The inherent rigidity of this market structure, which is at odds with the global proliferation of multilateral platforms and the decentralization of finance, underscores the unique insights offered by our agent-based model. We explore the implications of market rigidity on market structure and consider the element of stability, in market design. This extends the ongoing discourse on complex financial trading environments, providing an enhanced understanding of their dynamics and implications.
A tool to improve the effectiveness and the efficiency of public spending is proposed here. In the 19th century banknotes had a serial number. However, in modern days the use of digital transactions that do not use physical currency has opened the possibility to digitally track almost each cent of the economy. In this article a serial number or tracking number for each cent, pence or any other monetary unit of the economy is proposed. Then, almost all cents can be tracked by recording the transactions in a public distributed ledger, rather than recording the amount of the transaction, the information recorded in the block of the transaction is the actual serial number or tracking number for each cent that changes ownership. In order to keep the privacy of the transaction, only generic identification of private companies and individuals are recorded along with generic information about the concept of transaction, the region and the date/time. A secondary public distributed ledger whose blocks are identified by a hash reference that is recorded in the bank statement available to the payer and the payee allows for checking the accuracy of the first public distributed ledger by comparing the transactions made in one day, one region and one type of concept. However, the transactions made or received by the government are recorded with a much higher level of detail in the first ledger and a higher level of disclosure in the second ledger. The result is a tool that is able to accurately track public spending, to keep privacy of individuals and companies and to make statistical analysis and experiments or real tests in the economy of a country. This tool has the potential to assist public policymakers in demonstrating the societal benefits resulting from their policies, thereby enabling more informed decision-making for future policy endeavours.
The chapter begins by introducing the concept of virtual economies and their growing significance in the metaverse. It highlights the pivotal role played by cryptocurrencies, such as Bitcoin, in transforming the landscape of virtual transactions. The benefits and challenges of using cryptocurrencies as a medium of exchange in virtual worlds are discussed, alongside the disruptive potential of blockchain technology in enabling secure and decentralized transactions. Furthermore, the chapter delves into the integration of virtual currencies within online gaming platforms, where virtual economies have thrived. It explores the evolution of in-game currencies and the monetization models employed by game developers. The emergence of virtual marketplaces is also examined, wherein users can buy, sell, and trade digital assets. The significance of non-fungible tokens (NFTs) in establishing ownership and uniqueness of digital assets is explored within this context. The real-world impact and economic significance of virtual economies are then analyzed. The chapter investigates how virtual economies have influenced various industries, including gaming, entertainment, and art. It delves into revenue generation and job creation within these virtual economies, showcasing their potential to disrupt traditional financial systems. The chapter also acknowledges the challenges and risks associated with virtual economies. Issues such as fraud and regulatory concerns are discussed, along with potential scalability and interoperability obstacles. Finally, the chapter concludes by summarizing key points and providing insights into future trends and developments in virtual economies. It emphasizes the transformative potential of these economies, offering a glimpse into the promising and complex future of the metaverse.