Using a Quantum Annealer To Solve The Optimal Trading Trajectory
“Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer” by Peter Carr & Marcos Lopez de Prado our 2023 Quant of The Year, Gili Rosenberg, Poya Haghnegahdar, Kesheng Wu, Phil Goddard addresses a significant challenge in the realm of financial optimization. Moreover, the attempt of solving a multi-period portfolio optimization problem with a quantum annealer.
Representing a departure from traditional methods, which typically rely on continuous-variable formulations and classical optimization techniques.
The core problem tackled by the authors involves an asset manager seeking to invest a certain amount of capital across multiple assets over a defined investment horizon. Which is divided into discrete time steps.
With an objective to determine the optimal investment strategy that maximizes returns while minimizing risks and transaction costs. Including both temporary and permanent market impacts.
This paper argues that traditional mean-variance portfolio optimization problems solved as continuous-variable problems may not be an ideal approach for scenarios where assets are traded in large blocks or “even” lots. Which is common among institutional investors.
This discrete nature of the problem makes it inherently non-convex and significantly more challenging to solve than its continuous counterpart.
The authors present a formulation of the multi-period portfolio optimization problem as a quadratic integer optimization problem, suitable for solution via quantum annealing. They explore several integer encoding schemes to represent the discrete decision variables required by the quantum annealer.
Peter Carr Marcos Lopez de Prado et al. demonstrate that the quantum annealer can achieve high success rates in solving the optimization problem. These examples highlight the effectiveness of the quantum annealing approach in dealing with the discrete and non-convex nature of the problem.
A key limitation identified in the paper is the current state of quantum annealing technology!
As a result, which restricts the size of the problems that can be effectively solved. Despite these limitations, Peter Carr Marcos Lopez de Prado et al. express optimism that future advancements in quantum hardware will enable the solution of larger and more complex optimization problems.
Advantages Over Classical Methods?
One of the main advantages of the quantum annealing approach, as highlighted by the authors, is its ability to handle ill-conditioned or degenerate covariance matrices. Furthermore, without requiring their inversion, a common challenge in classical optimization methods.
Peter Carr Marcos Lopez de Prado et al. make a compelling case for the potential of quantum annealing to solve complex multi-period portfolio optimization problems. Demonstrates the feasibility of this approach through numerical examples. In addition, provides insights into how future technological advancements could further enhance its applicability.
As quantum hardware continues to evolve, this work will become increasingly capable of addressing larger and more intricate optimization problems that are currently intractable for classical computers!
Read the full paper:
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