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In this paper, a convex optimization-based method is proposed for numerically solving dynamic programs in continuous state and action spaces. The key idea is to approximate the output of the Bellman operator at a particular state by the…
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…
Linear Fisher markets are a fundamental economic model with applications in fair division as well as large-scale Internet markets. In the finite-dimensional case of $n$ buyers and $m$ items, a market equilibrium can be computed using the…
The system operator's scheduling problem in electricity markets, called unit commitment, is a non-convex mixed-integer program. The optimal value function is non-convex, preventing the application of traditional marginal pricing theory to…
We consider the problem of optimally executing a user trade over networks of constant function market makers (CFMMs) in the presence of hooks. Hooks, introduced in an upcoming version of Uniswap, are auxiliary smart contracts that allow for…
Automated market makers (AMM) have grown to obtain significant market share within the cryptocurrency ecosystem, resulting in a proliferation of new products pursuing exotic strategies for horizontal differentiation. Yet, their theoretical…
We propose a convex formulation for a trading system with the Conditional Value-at-Risk as a risk-adjusted performance measure under the notion of Direct Reinforcement Learning. Due to convexity, the proposed approach can uncover a…
A programmable quantum processor is a fundamental model of quantum computation. In this model, any quantum channel can be approximated by applying a fixed universal quantum operation onto an input state and a quantum `program' state, whose…
Automated market makers with concentrated liquidity capabilities are programmable at the tick level. The maximization of earned fees, plus depreciated reserves, is a convex optimization problem whose vector solution gives the best provision…
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…
This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…
Market simulator tries to create high-quality synthetic financial data that mimics real-world market dynamics, which is crucial for model development and robust assessment. Despite continuous advancements in simulation methodologies, market…
Prediction markets are powerful mechanisms for information aggregation, but existing designs are optimized for single-event contracts. In practice, traders frequently express beliefs about joint outcomes - through parlays in sports,…
We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it…
The circumcentered-reflection method (CRM) has been recently proposed as a methodology for accelerating several algorithms for solving the Convex Feasibility Problem (CFP), equivalent to finding a common fixed-point of the orthogonal…
Automated Market Makers (AMMs) are an integral component of the decentralized finance (DeFi) ecosystem, as they allow users to exchange crypto-assets without the need for trusted authorities or external price oracles. Although these…
We establish existence of Predictable Forward Performance Processes (PFPPs) in complete markets, which has been previously shown only in the binomial setting. Our market model can be a discrete-time or a continuous-time model, and the…
The Dynamic Function Market Maker (DFMM) introduced a fully automated framework for operating a multi-asset market, wherein an algorithmic accounting asset was used to connect different liquidity pools and ensure efficient rebalancing of…
Prediction markets allow traders to bet on potential future outcomes. These markets exist for weather, political, sports, and economic forecasting. Within this work we consider a decentralized framework for prediction markets using…
A descent algorithm, "Quasi-Quadratic Minimization with Memory" (QQMM), is proposed for unconstrained minimization of the sum, $F$, of a non-negative convex function, $V$, and a quadratic form. Such problems come up in regularized…