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We study the dynamic portfolio selection of an investor who uses deep learning methods to forecast stock market excess returns. In a two-asset allocation problem, deep neural networks -- both feedforward and long short-term memory (LSTM)…
We present a comprehensive framework that unifies several research areas within the context of vertex-weighted bipartite graphs, providing deeper insights and improved solutions. The fundamental solution concept for each problem involves…
This paper proposes a Deep Reinforcement Learning algorithm for financial portfolio trading based on Deep Q-learning. The algorithm is capable of trading high-dimensional portfolios from cross-sectional datasets of any size which may…
We present the first parallel algorithm for solving systems of linear equations in symmetric, diagonally dominant (SDD) matrices that runs in polylogarithmic time and nearly-linear work. The heart of our algorithm is a construction of a…
Deep neural networks (DNNs) have been used to model complex optimization problems in many applications, yet have difficulty guaranteeing solution optimality and feasibility, despite training on large datasets. Training a NN as a surrogate…
One of the most fundamental questions in quantitative finance is the existence of continuous-time diffusion models that fit market prices of a given set of options. Traditionally, one employs a mix of intuition, theoretical and empirical…
This paper studies Markov perfect equilibria in a repeated duopoly model where sellers choose algorithms. An algorithm is a mapping from the competitor's price to own price. Once set, algorithms respond quickly. Customers arrive randomly…
Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the…
We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our…
The simplex algorithm is one of the most popular algorithms to solve linear programs (LPs). Starting at an extreme point solution of an LP, it performs a sequence of basis exchanges (called pivots) that allows one to move to a better…
$\newcommand{\eps}{\varepsilon}$We present an auction algorithm using multiplicative instead of constant weight updates to compute a $(1-\eps)$-approximate maximum weight matching (MWM) in a bipartite graph with $n$ vertices and $m$ edges…
We present an algorithm that given a linear program with $n$ variables, $m$ constraints, and constraint matrix $A$, computes an $\epsilon$-approximate solution in $\tilde{O}(\sqrt{rank(A)}\log(1/\epsilon))$ iterations with high probability.…
Decentralized exchanges, such as those employing constant product market makers (CPMMs) like Uniswap V2, play a crucial role in the blockchain ecosystem by enabling peer-to-peer token swaps without intermediaries. Despite the increasing…
We propose a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, by making an analogy between the BSDE and reinforcement learning with the…
The beer game is a widely used in-class game that is played in supply chain management classes to demonstrate the bullwhip effect. The game is a decentralized, multi-agent, cooperative problem that can be modeled as a serial supply chain…
We analyze approximation rates by deep ReLU networks of a class of multi-variate solutions of Kolmogorov equations which arise in option pricing. Key technical devices are deep ReLU architectures capable of efficiently approximating tensor…
We present a new algorithm for computing hyperexponential solutions of ordinary linear differential equations with polynomial coefficients. The algorithm relies on interpreting formal series solutions at the singular points as analytic…
In this work we apply the Deep Galerkin Method (DGM) described in Sirignano and Spiliopoulos (2018) to solve a number of partial differential equations that arise in quantitative finance applications including option pricing, optimal…
We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive…
Over the last decade, combinatorial algorithms have been obtained for exactly solving several nonlinear convex programs. We first provide a formal context to this activity by introducing the notion of {\em rational convex programs} -- this…