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Stochastic Model Predictive Control And Portfolio Optimization

Author

Listed:
  • FLORIAN HERZOG

    (ETH Zurich, CH-8092 Zürich, Switzerland;
    SwissQuant Group AG, CH-8006 Zürich, Switzerland)

  • GABRIEL DONDI

    (ETH Zurich, CH-8092 Zürich, Switzerland;
    SwissQuant Group AG, CH-8006 Zürich, Switzerland)

  • HANS P. GEERING

    (ETH Zurich, CH-8092 Zürich, Switzerland)

Abstract

This paper proposes a solution method for the discrete-time long-term dynamic portfolio optimization problem with state and asset allocation constraints. We use the ideas of Model Predictive Control (MPC) to solve the constrained stochastic control problem. MPC is a solution technique which was developed to solve constrained optimal control problems for deterministic control applications. MPC solves the optimal control problem with a receding horizon where a series of consecutive open-loop optimal control problems is solved.The aim of this paper is to develop an MPC approach to the problem of long-term portfolio optimization when the expected returns of the risky assets are modeled using a factor model based on stochastic Gaussian processes. We prove that MPC is a suboptimal control strategy for stochastic systems which uses the new information advantageously and thus is better than the pure optimal open-loop control. For the open-loop optimal control optimization, we derive the conditional portfolio distribution and the corresponding conditional portfolio mean and variance. The mean and the variance depend on future decision about the asset allocation.For the dynamic portfolio optimization problem, we consider constraints on the asset allocation as well as probabilistic constraints on the attainable values of the portfolio wealth. We discuss two different objectives, a classical mean–variance objective and the objective to maximize the probability of exceeding a predetermined value of the portfolio. The dynamic portfolio optimization problem is stated, and the solution via MPC is explained in detail. The results are then illustrated in a case study.

Suggested Citation

  • Florian Herzog & Gabriel Dondi & Hans P. Geering, 2007. "Stochastic Model Predictive Control And Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 203-233.
    • Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:02:n:s0219024907004196
    DOI: 10.1142/S0219024907004196
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    References listed on IDEAS

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    1. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
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    Cited by:

    1. Vladimir Dombrovskii & Tatyana Obedko, 2014. "Portfolio Optimization in the Financial Market with Correlated Returns under Constraints, Transaction Costs and Different Rates for Borrowing and Lending," Papers 1410.8042, arXiv.org.
    2. Razvan Oprisor & Roy Kwon, 2020. "Multi-Period Portfolio Optimization with Investor Views under Regime Switching," JRFM, MDPI, vol. 14(1), pages 1-31, December.
    3. Yuji Yamada & James A. Primbs, 2018. "Model Predictive Control for Optimal Pairs Trading Portfolio with Gross Exposure and Transaction Cost Constraints," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 25(1), pages 1-21, March.
    4. Khemka, Gaurav & Steffensen, Mogens & Warren, Geoffrey J., 2021. "How sub-optimal are age-based life-cycle investment products?," International Review of Financial Analysis, Elsevier, vol. 73(C).
    5. Vladimir Dombrovskii & Tatyana Obyedko, 2014. "Dynamic Investment Portfolio Optimization under Constraints in the Financial Market with Regime Switching using Model Predictive Control," Papers 1410.1136, arXiv.org.
    6. Peter Nystrup & Stephen Boyd & Erik Lindström & Henrik Madsen, 2019. "Multi-period portfolio selection with drawdown control," Annals of Operations Research, Springer, vol. 282(1), pages 245-271, November.
    7. Dimitris Bertsimas & Bartolomeo Stellato, 2022. "Online Mixed-Integer Optimization in Milliseconds," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2229-2248, July.

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