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On Quantum Ambiguity and Potential Exponential Computational Speed-Ups to Solving Dynamic Asset Pricing Models

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  • Eric Ghysels
  • Jack Morgan

Abstract

We formulate quantum computing solutions to a large class of dynamic nonlinear asset pricing models using algorithms, in theory exponentially more efficient than classical ones, which leverage the quantum properties of superposition and entanglement. The equilibrium asset pricing solution is a quantum state. We introduce quantum decision-theoretic foundations of ambiguity and model/parameter uncertainty to deal with model selection.

Suggested Citation

  • Eric Ghysels & Jack Morgan, 2024. "On Quantum Ambiguity and Potential Exponential Computational Speed-Ups to Solving Dynamic Asset Pricing Models," Papers 2405.01479, arXiv.org, revised May 2024.
  • Handle: RePEc:arx:papers:2405.01479
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    References listed on IDEAS

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    1. Lars Peter Hansen & Thomas J Sargent, 2014. "Beliefs, Doubts and Learning: Valuing Macroeconomic Risk," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 10, pages 331-377, World Scientific Publishing Co. Pte. Ltd..
    2. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2013. "Ambiguity and robust statistics," Journal of Economic Theory, Elsevier, vol. 148(3), pages 974-1049.
      • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Ambiguity and Robust Statistics," Working Papers 382, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    3. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    4. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, vol. 77(1), pages 177-234, January.
    5. Ole E. Barndorff‐Nielsen & Richard D. Gill & Peter E. Jupp, 2003. "On quantum statistical inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 775-804, November.
    6. Leland E. Farmer & Alexis Akira Toda, 2017. "Discretizing nonlinear, non‐Gaussian Markov processes with exact conditional moments," Quantitative Economics, Econometric Society, vol. 8(2), pages 651-683, July.
    7. Lilia Maliar & Serguei Maliar, 2015. "Merging simulation and projection approaches to solve high‐dimensional problems with an application to a new Keynesian model," Quantitative Economics, Econometric Society, vol. 6(1), pages 1-47, March.
    8. Nikolay Gospodinov & Damba Lkhagvasuren, 2014. "A Moment‐Matching Method For Approximating Vector Autoregressive Processes By Finite‐State Markov Chains," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 843-859, August.
    9. Lars Peter Hansen & John C. Heaton & Nan Li, 2008. "Consumption Strikes Back? Measuring Long-Run Risk," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 260-302, April.
    10. Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.
    11. Oechssler, Jörg & Roomets, Alex, 2015. "A test of mechanical ambiguity," Journal of Economic Behavior & Organization, Elsevier, vol. 119(C), pages 153-162.
    12. Tommaso Denti & Luciano Pomatto, 2022. "Model and Predictive Uncertainty: A Foundation for Smooth Ambiguity Preferences," Econometrica, Econometric Society, vol. 90(2), pages 551-584, March.
    13. Lars Peter Hansen, 2007. "Beliefs, Doubts and Learning: Valuing Economic Risk," NBER Working Papers 12948, National Bureau of Economic Research, Inc.
    14. Basieva, Irina & Khrennikova, Polina & Pothos, Emmanuel M. & Asano, Masanari & Khrennikov, Andrei, 2018. "Quantum-like model of subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 150-162.
    15. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    16. Eichberger, Jürgen & Pirner, Hans Jürgen, 2018. "Decision theory with a state of mind represented by an element of a Hilbert space: The Ellsberg paradox," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 131-141.
    17. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
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