Learning to Maximize Gains From Trade in Small Markets
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Getting Started with Apache Spark: Deployment, Usage & Best Practices
Apache Spark has become one of the most popular open-source frameworks for big data processing, offering lightning-fast computation as well as impressive cluster scalability. Whether you’re new to Spark or looking to improve, this guide will walk you through Spark in detail: how to deploy it, how to use it effectively, and the best practices to follow for killer performance and easy maintainability.
An optimal investment strategy aimed at maximizing the expected utility across all intermediate capital levels
This study investigates an optimal investment problem for an insurance company operating under the Cramer-Lundberg risk model, where investments are made in both a risky asset and a risk-free asset. In contrast to other literature that focuses on optimal investment and/or reinsurance strategies to maximize the expected utility of terminal wealth within a given time horizon, this work considers the expected value of utility accumulation across all intermediate capital levels of the insurer. By employing the Dynamic Programming Principle, we prove a verification theorem, in order to show that any solution to the Hamilton-Jacobi-Bellman (HJB) equation solves our optimization problem. Subject to some regularity conditions on the solution of the HJB equation, we establish the existence of the optimal investment strategy. Finally, to illustrate the applicability of the theoretical findings, we present numerical examples.
Profit Maximization In Arbitrage Loops
Cyclic arbitrage chances exist abundantly among decentralized exchanges (DEXs), like Uniswap V2. For an arbitrage cycle (loop), researchers or practitioners usually choose a specific token, such as Ether as input, and optimize their input amount to get the net maximal amount of the specific token as arbitrage profit. By considering the tokens' prices from CEXs in this paper, the new arbitrage profit, called monetized arbitrage profit, will be quantified as the product of the net number of a specific token we got from the arbitrage loop and its corresponding price in CEXs. Based on this concept, we put forward three different strategies to maximize the monetized arbitrage profit for each arbitrage loop. The first strategy is called the MaxPrice strategy. Under this strategy, arbitrageurs start arbitrage only from the token with the highest CEX price. The second strategy is called the MaxMax strategy. Under this strategy, we calculate the monetized arbitrage profit for each token as input in turn in the arbitrage loop. Then, we pick up the most maximal monetized arbitrage profit among them as the monetized arbitrage profit of the MaxMax strategy. The third one is called the Convex Optimization strategy. By mapping the MaxMax strategy to a convex optimization problem, we proved that the Convex Optimization strategy could get more profit in theory than the MaxMax strategy, which is proved again in a given example. We also proved that if no arbitrage profit exists according to the MaxMax strategy, then the Convex Optimization strategy can not detect any arbitrage profit, either. However, the empirical data analysis denotes that the profitability of the Convex Optimization strategy is almost equal to that of the MaxMax strategy, and the MaxPrice strategy is not reliable in getting the maximal monetized arbitrage profit compared to the MaxMax strategy.
ChatGPT as Research Scientist: Probing GPT's Capabilities as a Research Librarian, Research Ethicist, Data Generator and Data Predictor
How good a research scientist is ChatGPT? We systematically probed the capabilities of GPT-3.5 and GPT-4 across four central components of the scientific process: as a Research Librarian, Research Ethicist, Data Generator, and Novel Data Predictor, using psychological science as a testing field. In Study 1 (Research Librarian), unlike human researchers, GPT-3.5 and GPT-4 hallucinated, authoritatively generating fictional references 36.0% and 5.4% of the time, respectively, although GPT-4 exhibited an evolving capacity to acknowledge its fictions. In Study 2 (Research Ethicist), GPT-4 (though not GPT-3.5) proved capable of detecting violations like p-hacking in fictional research protocols, correcting 88.6% of blatantly presented issues, and 72.6% of subtly presented issues. In Study 3 (Data Generator), both models consistently replicated patterns of cultural bias previously discovered in large language corpora, indicating that ChatGPT can simulate known results, an antecedent to usefulness for both data generation and skills like hypothesis generation. Contrastingly, in Study 4 (Novel Data Predictor), neither model was successful at predicting new results absent in their training data, and neither appeared to leverage substantially new information when predicting more versus less novel outcomes. Together, these results suggest that GPT is a flawed but rapidly improving librarian, a decent research ethicist already, capable of data generation in simple domains with known characteristics but poor at predicting novel patterns of empirical data to aid future experimentation.
Learning to Maximize Gains From Trade in Small Markets
We study the problem of designing a two-sided market (double auction) to maximize the gains from trade (social welfare) under the constraints of (dominant-strategy) incentive compatibility and budget-balance. Our goal is to do so for an unknown distribution from which we are given a polynomial number of samples. Our first result is a general impossibility for the case of correlated distributions of values even between just one seller and two buyers, in contrast to the case of one seller and one buyer (bilateral trade) where this is possible. Our second result is an efficient learning algorithm for one seller and two buyers in the case of independent distributions which is based on a novel algorithm for computing optimal mechanisms for finitely supported and explicitly given independent distributions. Both results rely heavily on characterizations of (dominant-strategy) incentive compatible mechanisms that are strongly budget-balanced.
High order universal portfolios
The Cover universal portfolio (UP from now on) has many interesting theoretical and numerical properties and was investigated for a long time. Building on it, we explore what happens when we add this UP to the market as a new synthetic asset and construct by recurrence higher order UPs. We investigate some important theoretical properties of the high order UPs and show in particular that they are indeed different from the Cover UP and are capable to break the time permutation invariance. We show that under some perturbation regime the second high order UP has better Sharp ratio than the standard UP and briefly investigate arbitrage opportunities thus created. Numerical experiences on a benchmark from the literature confirm that high order UPs improve Cover's UP performances.