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Duality of linear programming is a standard approach to the classical weighted maximum matching problem. From an economic perspective, the dual variables can be regarded as prices of products and payoffs of buyers in a two-sided matching…
We study two-sided many-to-one matching markets with transferable utilities, e.g., labor and rental housing markets, in which money can exchange hands between agents, subject to distributional constraints on the set of feasible allocations.…
We construct an empirically founded model of a repo trade intermediated by two broker-dealers and prove multiple equilibrium and the existence of equilibrium at the joint profit maximizing volume of trade. We then present a smart contract…
With the increasing demand for computationally intensive services like deep learning tasks, emerging distributed computing platforms such as edge computing (EC) systems are becoming more popular. Edge computing systems have shown promising…
We prove that the classic problem of finding a competitive equilibrium in an exchange economy with indivisible goods, money, and unit-demand agents is PPAD-complete. In this "housing market", agents have preferences over the house and…
Matching algorithms have demonstrated great success in several practical applications, but they often require centralized coordination and plentiful information. In many modern online marketplaces, agents must independently seek out and…
We develop a methodology that utilizes deep learning to simultaneously solve and estimate canonical continuous-time general equilibrium models in financial economics. We illustrate our method in two examples: (1) industrial dynamics of…
A symbolic computational algorithm which detects " linear "` solutions of nonlinear polynomial differential equations of single functions, is developed throughout this paper.
An effective distribution electricity market (DEM) is required to manage the rapidly growing small-scale distributed energy resources (DERs) in distribution systems (DSs). This paper proposes a day-ahead DEM clearing and pricing mechanism…
We are interested in the optimal scheduling of a collection of multi-component application jobs in an edge computing system that consists of geo-distributed edge computing nodes connected through a wide area network. The scheduling and…
Current state-of-the-art solution techniques for solving bilevel optimization problems either assume strong problem regularity criteria or are computationally intractable. In this paper we address power system problems of bilevel structure,…
In recent years a large literature on deep learning based methods for the numerical solution partial differential equations has emerged; results for integro-differential equations on the other hand are scarce. In this paper we study deep…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
The presence of integer variables in the European day-ahead electricity market renders the social welfare maximization problem non-convex and non-differentiable, making classical marginal pricing theoretically inconsistent. Existing pricing…
Can deep reinforcement learning algorithms be exploited as solvers for optimal trading strategies? The aim of this work is to test reinforcement learning algorithms on conceptually simple, but mathematically non-trivial, trading…
This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…
We investigate the portfolio selection problem for an agent with rank-dependent utility in an incomplete financial market. For a constant-coefficient market and CRRA utilities, we characterize the deterministic strict equilibrium…
Execution algorithms are vital to modern trading, they enable market participants to execute large orders while minimising market impact and transaction costs. As these algorithms grow more sophisticated, optimising them becomes…
Two-dimensional (2D) Multiple Signal Classification algorithm is a powerful technique for high-resolution direction-of-arrival (DOA) estimation in array signal processing. However, the exhaustive search over the 2D an-gular domain leads to…
Online bipartite matching is a fundamental problem in online algorithms. The goal is to match two sets of vertices to maximize the sum of the edge weights, where for one set of vertices, each vertex and its corresponding edge weights appear…