Abstract Bitcoin provides its users with transaction-processing services which are similar to those of traditional payment systems. This article models the novel economic structure implied by Bitcoin’s innovative decentralized design, allows system be reliably operated unrelated parties called miners. We find that this design protects from monopoly pricing. Competition among service providers within platform and free entry imply no entity can profitably affect level fees paid users. Instead,...

We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network. establish convergence, characterize the convergence rate regular graphs, and demonstrate that exhibits better scaling properties than pairwise averaging, alternative has received much recent attention. Consensus propagation can be viewed as special case of belief our results contribute to literature. In particular, beyond singly-connected there are very few classes relevant problems...

Systemic risk refers to the of collapse an entire complex system as a result actions taken by individual component entities or agents that comprise system. is issue great concern in modern financial markets well as, more broadly, management business and engineering systems. We propose axiomatic framework for measurement systemic based on simultaneous analysis outcomes across over scenarios nature. Our defines broad class measures accomodate rich set regulatory preferences. This general...

Bitcoin provides its users with transaction-processing services which are similar to those of traditional payment systems. This paper models the novel economic structure implied by Bitcoin's innovative decentralized design, allows system be reliably operated unrelated parties called miners. We find that this design protects from monopoly pricing. Competition among service providers within platform and free entry imply no entity can profitably affect level fees paid users. Instead, a market...

We analyze the computational problem of estimating financial risk in a nested simulation. In this approach, an outer simulation is used to generate scenarios, and inner estimate future portfolio values each scenario. focus on one measure, probability large loss, we propose new algorithm risk. Our sequentially allocates effort based marginal changes estimator Theoretical results are given show that has faster convergence order compared conventional uniform sampling approach. Numerical...

This paper presents a novel, non-parametric approximate dynamic programming (ADP) algorithm that enjoys dimension-independent approximation and sample complexity guarantees. We obtain this by “kernelizing” recent mathematical program for ADP (the “smoothed linear program”). Loosely, our guarantees show we can exchange the importance of choosing good architecture priori (as required existing approaches) with sampling effort. also present simple active set solving resulting quadratic program,...

We introduce the pathwise optimization (PO) method, a new convex procedure to produce upper and lower bounds on optimal value (the “price”) of high-dimensional stopping problem. The PO method builds dual characterization problems as over space martingales, which we dub martingale duality approach. demonstrate via numerical experiments that produces quality comparable with state-of-the-art approaches, but in fraction time required for those approaches. As by-product, it yields (and suboptimal...

We introduce a regression-based nested Monte Carlo simulation method for the estimation of financial risk. An outer level is used to generate risk factors and an inner price securities compute portfolio losses given factor outcomes. The mean squared error (MSE) standard converges at rate k −2/3 , where measures computational effort. proposed regression combines information from different realizations provide better estimate loss function. MSE −1 until reaching asymptotic bias which depends...

Owned by nobody and controlled an almost immutable protocol the Bitcoin payment system is a platform with two main constituencies: users profit seeking miners who maintain system's infrastructure. The paper seeks to understand economics of system: How does raise revenue pay for its infrastructure? are usage fees determined? much infrastructure deployed? What implications changing parameters in protocol? A simplified economic model that captures properties answers these questions. Transaction...

Automated market making (AMM) protocols such as Uniswap have recently emerged an alternative to the most common structure for electronic trading, limit order book. Relative books, AMMs are both more computationally efficient and do not require participation of active intermediaries. As such, dominant mechanism trust-less decentralized exchanges (DEXs). We develop a model underlying economics from perspective their passive liquidity providers (LPs). Our central contribution is "Black-Scholes...

We establish the convergence of min-sum message passing algorithm for minimization a quadratic objective function given convex decomposition. Our results also apply to equivalent problem Gaussian belief propagation.

We present a novel linear program for the approximation of dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on natural “projection” well-studied exact programming. Such programs restrict attention approximations that are lower bounds optimal function. Our program—the “smoothed program”—is distinct from such and relaxes restriction bounding an appropriate fashion while remaining computationally...

Modern electronic markets have been characterized by a relentless drive toward faster decision making. Significant technological investments led to dramatic improvements in latency, the delay between trading and resulting trade execution. We describe theoretical model for quantitative valuation of latency. Our measures frictions created presence considering optimal execution problem representative investor. Via dynamic programming analysis, our provides closed-form expression cost latency...

We consider a broad class of dynamic portfolio optimization problems that allow for complex models return predictability, transaction costs, trading constraints, and risk considerations. Determining an optimal policy in this general setting is almost always intractable. propose linear rebalancing rules describe efficient computational procedure to optimize with class. illustrate method the context execution show it achieves near performance. another numerical example involving mean-variance...

Regulatory changes are transforming the multitrillion dollar swaps market from a network of bilateral contracts to one in which cleared through central counterparties (CCPs). The stability new framework depends on CCPs’ resilience. Margin requirements CCP’s first line defense against default counterparty. To capture liquidity costs at default, margin need increase superlinearly position size. However, convex create an incentive for dealer split its positions across multiple CCPs, effectively...

We consider the problem of A-B testing when impact treatment is marred by a large number covariates. Randomization can be highly inefficient in such settings, and thus we optimally allocating test subjects to either with view maximizing precision our estimate effect. Our main contribution tractable algorithm for this online setting, where arrive, must assigned, sequentially, covariates drawn from an elliptical distribution finite second moment. further characterize gain afforded optimized...

We establish that the min-sum message-passing algorithm and its asynchronous variants converge for a large class of unconstrained convex optimization problems, generalizing existing results pairwise quadratic problems. The main sufficient condition is scaled diagonal dominance. This similar to known conditions convergence other decentralized algorithms, such as coordinate descent gradient descent.

We propose a simple approach to dynamic multi-period portfolio choice with transaction costs that is tractable in settings large number of securities, realistic return dynamics multiple risk factors, many predictor variables, and stochastic volatility. obtain closed-form solution for an optimal trading rule when the problem restricted broad class strategies we define as 'linearity generating strategies' (LGS). When this class, non-linear optimization reduces deterministic linear-quadratic...

The paper's introduction offers a high-level review of Bitcoin's features, especially its governance by protocol. paper proceeds to summarize analysis as payment system. It pays particular attention comparison between Bitcoin and firm-run

We consider the impact of trading fees on profits arbitrageurs against an automated marker (AMM) or, equivalently, adverse selection incurred by liquidity providers due to arbitrage. extend model Milionis et al. [2022] for a general class two asset AMMs both introduce and discrete Poisson block generation times. In our setting, we are able compute expected instantaneous rate arbitrage profit in closed form. When low, fast asymptotic regime, takes particularly simple form: simply scale down...

We consider an agent interacting with unmodeled environment. At each time, the makes observation, takes action, and incurs a cost. Its actions can influence future observations costs. The goal is to minimize long-term average propose novel algorithm, known as active LZ for optimal control based on ideas from Lempel-Ziv scheme universal data compression prediction. establish that, under if there exists integer <i xmlns:mml="http://www.w3.org/1998/Math/MathML"...

Many financial markets operate as electronic limit order books under a price-time priority rule. In this setting, among all resting orders awaiting trade at given price, earlier are prioritized for matching with contra-side liquidity takers. This creates technological arms race high-frequency traders and other automated market participants to establish early (and hence advantageous) positions in the resulting first-in-first-out (FIFO) queue. We develop model valuing based on their relative...