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Applications of MPC to Finance

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Handbook of Model Predictive Control

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Abstract

This chapter describes the application of Model Predictive Control (MPC) to the finance problems of portfolio optimization and dynamic option hedging. Both of these problems are naturally formulated in the context of stochastic control, where, under idealized market settings, closed-form solutions have been found. However, realistic trading in financial markets is naturally a constrained environment. Moreover, models of stock price movement can be complex and not subject to analytical expression, while issues such as transaction costs can significantly affect the performance of trading strategies. These considerations have led to the development and successful application of MPC methods. Here, we develop the relevant system dynamics for trading, and present basic MPC formulations for both the portfolio optimization and dynamic option hedging problems. Key issues in the use of MPC for these problems and pointers to the literature provide the necessary background for those in the MPC community to begin to contribute to this exciting application area.

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Notes

  1. 1.

    In this chapter we will limit our discussion to the trading of stocks, but the formulations presented directly translate to the trading of other securities as well.

  2. 2.

    We assume that the trader’s actions do not affect stock prices, which is referred to as being a price taker, otherwise we would require a model for stock prices that depends on the buying and selling of the trader.

  3. 3.

    Due to a lack of liquidity, large market orders will sometimes transact at prices that are worse than the existing bid or ask. This represents a further cost.

  4. 4.

    For example, short selling is not possible in Individual Retirement Accounts (IRAs) in the US.

  5. 5.

    More specifically, it leads to the concept of the absence of arbitrage price for the option. See [16] or [28].

References

  1. Bemporad, A., Gabbriellini, T., Puglia, L., Bellucci, L.: Scenario based stochastic model predictive control for dynamic option hedging. In: Proceedings of 49th IEEE Conference on Decision and Control, Atlanta (2010)

    Google Scholar 

  2. Bemporad, A., Puglia, L., Gabbriellini, T.: A stochastic model predictive control approach to dynamic option hedging with transaction costs. In: Proceedings of American Control Conference, San Francisco (2011)

    Google Scholar 

  3. Bemporad, A., Bellucci, L., Gabbriellini, T.: Dynamic option hedging via stochastic model predictive control based on scenario simulation. Quant. Finan. 14(10), 1739–1751 (2014)

    Article  MathSciNet  Google Scholar 

  4. Black, F., Scholes, M.: Pricing of options and corporate liabilities. Eur. J. Polit. Econ. 81(3), 637–654 (1973)

    Article  MathSciNet  Google Scholar 

  5. Calafiore, G.C.: Multi-period portfolio optimization with linear control policies. Automatica 44, 2463–2473 (2008)

    Article  Google Scholar 

  6. Calafiore, G.C.: An affine control method for optimal dynamic asset allocation with transaction costs. SIAM J. Control Optim. 48(4), 2254–2274 (2009)

    Article  MathSciNet  Google Scholar 

  7. Dombrovskii, V.V., Obyedko, T.Y.: Predictive control of systems with Markovian jumps under constraints and its application to the investment portfolio optimization. Autom. Remote Control 72(5), 989–1003 (2011)

    Article  MathSciNet  Google Scholar 

  8. Dombrovskii, V.V., Odyedko, T.Y.: Model predictive control for constrained systems with serially correlated stochastic parameters and portfolio optimization. Automatica 54, 325–331 (2015)

    Article  MathSciNet  Google Scholar 

  9. Dombrovskii, V.V., Dombrovskii, D.V., Lyashenko, E.A.: Investment portfolio optimisation with transaction costs and constraints using model predictive control. In: Proceedings of the 8th Russian-Korean International Symposium on Science and Technology, pp. 202–205 (2004)

    Google Scholar 

  10. Dombrovskii, V.V., Dombrovskii, D.V., Lyashenko, E.A.: Predictive control of random-parameter systems with multiplicative noise: application to investment portfolio optimization. Autom. Remote Control 66, 583–595 (2005)

    Article  MathSciNet  Google Scholar 

  11. Dombrovskii, V.V., Dombrovskii, D.V., Lyashenko, E.A.: Model predictive control of systems random dependent parameters under constraints and its application to the investment portfolio optimization. Autom. Remote Control 67, 1927–1939 (2006)

    Article  MathSciNet  Google Scholar 

  12. Herzog, F., Keel, S., Dondi, G., Schumann, L.M., Geering, H.P.: Model predictive control for portfolio selection. In: Proceedings of the 2006 American Control Conference, Minneapolis, pp. 1252–1259 (2006)

    Google Scholar 

  13. Herzog, F., Dondi, G., Geering, H.P.: Stochastic model predictive control and portfolio optimization. Int. J. Theor. Appl. Finance 10(2), 203–233 (2007)

    Article  MathSciNet  Google Scholar 

  14. Hull, J.C.: Options, Futures, and Other Derivatives, 9th edn. Pearson, New York (2014)

    MATH  Google Scholar 

  15. Lee, J.H.: Dynamic portfolio management with private equity funds. PhD thesis, Stanford University (2012)

    Google Scholar 

  16. Luenberger, D.G.: Investment Science, 2nd edn. Oxford University Press, Oxford (2013)

    Google Scholar 

  17. Markowitz, H.: Portfolio selection. J. Finance 7(1), 77–91 (1952)

    Google Scholar 

  18. Meindl, P.: Portfolio optimization and dynamic hedging with receding horizon control, stochastic programming, and Monte Carlo simulation. PhD thesis, Stanford University (2006)

    Google Scholar 

  19. Meindl, P., Primbs, J.: Dynamic hedging with stochastic volatility using receding horizon control. In: Proceedings of Financial Engineering Applications, Cambridge, MA, pp. 142–147 (2004)

    Google Scholar 

  20. Meindl, P., Primbs, J.: Dynamic hedging of single and multi-dimensional options with transaction costs: a generalized utility maximization approach. Quant. Finan. 8(3), 299–312 (2008)

    Article  MathSciNet  Google Scholar 

  21. Merton, R.C.: Optimum consumption and portfolio rules in a continuous-time model. J. Econ. Theory 3(4), 373–413 (1971)

    Article  MathSciNet  Google Scholar 

  22. Merton, R.C.: Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4, 142–183 (1973)

    Article  MathSciNet  Google Scholar 

  23. Oksendal, B.: Stochastic Differential Equations: An Introduction with Applications, 6th edn. Springer, Berlin (2010)

    MATH  Google Scholar 

  24. Piccoli, B., Marigo, A.: Model predictive control for portfolio optimization. In: Proceedings of 2nd IFAC Symposium on System, Structure and Control (2004)

    Google Scholar 

  25. Primbs, J.: Portfolio optimization applications of stochastic receding horizon control. In: Proceedings of American Control Conference, pp. 1811–1816 (2007)

    Google Scholar 

  26. Primbs, J.: Dynamic hedging of basket options under proportional transaction costs. Int. J. Control 82(10), 1841–1855 (2009)

    Article  MathSciNet  Google Scholar 

  27. Primbs, J.: LQR and receding horizon approaches to multi-dimensional option hedging under transaction costs. In: Proceedings of American Control Conference, pp. 6891–6896 (2010)

    Google Scholar 

  28. Primbs, J.A.: A Factor Model Approach to Derivative Pricing. CRC Press, West Palm Beach (2016)

    MATH  Google Scholar 

  29. Primbs, J., Sung, C.H.: A stochastic receding horizon control approach to constrained index tracking. Asia-Pacific Finan. Markets 15(1), 3–24 (2008)

    Article  Google Scholar 

  30. Samuelson, P.A.: Lifetime portfolio selection by dynamic stochastic programming. Rev. Econ. Stat. 51(3), 239–246 (1969)

    Article  Google Scholar 

  31. Sridharan, S., Chitturi, D., Rodriguez, A.A.: A receding horizon control approach to portfolio optimization using a risk-minimax objective for wealth tracking. In: Proceedings of IEEE Conference on Control Applications, Denver, pp. 1282–1287 (2011)

    Google Scholar 

  32. Wonham, W.M.: Optimal stationary control of a linear system with state-dependent noise. SIAM J. Control Optim. 5, 486–500 (1967)

    Article  MathSciNet  Google Scholar 

  33. Yamada, Y., Primbs, J.: Model predictive control for optimal portfolios with cointegrated pairs of stocks. In: Proceedings of the 51st IEEE Conference on Decision and Control, pp. 5705–5710 (2012)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Finance, Mihaylo College of Business and Economics, California State University Fullerton, Fullerton, CA, 92831, USA

    James A. Primbs

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  1. James A. Primbs
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Correspondence to James A. Primbs .

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Editors and Affiliations

  1. Independent Researcher, London, UK

    Saša V. Raković

  2. Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA

    William S. Levine

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Primbs, J.A. (2019). Applications of MPC to Finance. In: Raković, S., Levine, W. (eds) Handbook of Model Predictive Control. Control Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-77489-3_27

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  • DOI: https://doi.org/10.1007/978-3-319-77489-3_27

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  • Publisher Name: Birkhäuser, Cham

  • Print ISBN: 978-3-319-77488-6

  • Online ISBN: 978-3-319-77489-3

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