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We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs (including permanent and temporary market impact), and,… (More)

We introduce Stochastic Flow Diagrams (SFDs), a new mathematical approach to represent complex dynamic systems into a single weighted digraph. This topological representation provides a way to visualize what otherwise would be a morass of equations in differences. SFDs model the propagation and reverberation that follows a shock. For example, reverberation… (More)

A large portion of Macroeconomic and Financial research is built upon classical applications of Linear Algebra (such as regression analysis) and Stochastic Calculus (such as valuation models). As a result, most Macroeconomic and Financial research has inherited a focus on geometric locations rather than logical relations. Ideally, Econometric models could… (More)

Most popular analysis tools on time series require the data to be taken at uniform time intervals. However, the real-world time series, such as those from financial markets, are typically taken at irregular time intervals. It is a common practice to resample or bin the irregular time series into a regular one, but there are significant limitations on this… (More)

________________________________ The views expressed in this publication are the authors' and do not necessarily reflect the opinion of Tudor Investment Corporation. We would like to thank the Managing Editor of Algorithmic Finance, Prof. Philip Maymin (New York University-Polytechnic Institute), as well as two anonymous referees, for their insightful… (More)

Portfolio optimization is one of the problems most frequently encountered by financial practitioners. The main goal of this paper is to fill a gap in the literature by providing a well-documented, step-by-step open-source implementation of Critical Line Algorithm (CLA) in scientific language. The code is implemented as a Python class object, which allows it… (More)

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