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A Stochastic Control Model for the Average Price of Manufacturer Sales on Commodity Exchanges

  • Control in Social Economic Systems
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Abstract

We propose an approach for controlling the weighted average price of a manufacturers sales on commodity exchanges. This problem is highly relevant due to the need for the manufacturer to hedge their profits in case of a sharp drop in market prices. We consider applications of the proposed control to executing trading operations on real commodity exchanges in order to demonstrate its efficiency.

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References

  1. Øksendal, B., Stochastic Differential Equations. An Introduction with Applications, Berlin: Springer-Verlag, 2003, 5th ed. Translated under the title Stokhasticheskie differentsial’nye uravneniya. Vvedenie v teoriyu i prilozheniya, Moscow: Mir, 2003.

    MATH  Google Scholar 

  2. Borodin, A.N., Sluchainye protsessy (Random Processes), St. Petersburg: Lan’, 2013.

    Google Scholar 

  3. Shiryaev, A.N., Osnovy stokhasticheskoi finansovoi matematiki (Fundamentals of Stochastic Financial Mathematics), Moscow: Fazis, 1998, vols. 1, 2.

    Google Scholar 

  4. Vavilov, S.A., On the Probability Models to Control the Investor Portfolio, in Asymptotic Methods in Probability and Statistics with Applications, Balakrishnan, N., Ibragimov, I.A., and Nevzorov, V.B., Eds., Boston: Birkhauser, 2001, pp. 535–547.

    Chapter  Google Scholar 

  5. Vavilov, S.A. and Ermolenko, K.Yu., On the New Stochastic Approach to Control the Investment Portfolio, IAENG I. J. A. M., 2008, vol. 38, no. 1, pp. 54–62. https://doi.org/www.iaeng.org/IJAM/issues_v38/issue_1/IJAM_38_1_09.pdf

    MathSciNet  MATH  Google Scholar 

  6. Vavilov, S.A. and Ermolenko, K.Yu., Finansovaya matematika. Stokhasticheskii analiz (Financial Mathematics. Stochastic Analysis), Moscow: Yurait, 2016.

    Google Scholar 

  7. Fleming, W.H. and Rishel, R.W., Deterministic and Stochastic Optimal Control, Berkin: Springer-Verlag, 1975. Translated under the title Optimal’noe upravlenie determinirovannymi i stokhasticheskimi sistemami, Moscow: Mir, 1978.

    Book  MATH  Google Scholar 

  8. Karatzas, I., Lehoczky, J.P., and Shreve, S.E., Optimal Portfolio and Consumption Decisions for a “Small Investor” on a Finite Horizon, SIAM J. Control Optim., 1987, vol. 25, no. 6, pp. 1557–1586.

    Article  MathSciNet  MATH  Google Scholar 

  9. Kamke, E., Differentialgleichungen. L¨osungsmethoden und L¨osungen, Leipzig: Akademische Verlagsgesellschaft, 1959. Translated under the title Spravochnik po obyknovennym differential’nym uravneniyam, Moscow: Nauka, 1976.

    Google Scholar 

  10. Tikhonov, A.N., Goncharskii, A.V., Stepanov, V.V., and Yagola, A.G., Chislennye metody resheniya nekorrektnykh zadach (Numerical Methods for Solving Ill-Posed Problems), Moscow: Nauka, 1990.

    MATH  Google Scholar 

  11. Zhang, L., Mykland, A., and Ait-Sahalia, Y., A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High-Frequency Data, J. Am. Stat. Ass., 2005, vol. 100, no. 472, pp. 1394–1411.

    Article  MathSciNet  MATH  Google Scholar 

  12. Vavilov, S.A. and Ermolenko, K.Yu., On One Approach to the Nonparametric Estimation Problem in the Statistics of Random Processes Based on the Method of the Ill-Posed Problem, Zap. Nauchn. Seminarov POMI, 2007, vol. 351, pp. 117–129.

    Google Scholar 

  13. Merton, R., Option Pricing when Underlying Stock Returns are Discontinuous, J. Finan. Econom., 1976, vol. 3, pp. 125–144.

    Article  MATH  Google Scholar 

  14. Heston, S.L., A Closed Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Option, Rev. Financ. Stud., 1993, vol. 6, no. 2, pp. 327–343.

    Article  MATH  Google Scholar 

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Correspondence to S. A. Vavilov or K. S. Kuznetsov.

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Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 6, pp. 142–155.

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Vavilov, S.A., Kuznetsov, K.S. A Stochastic Control Model for the Average Price of Manufacturer Sales on Commodity Exchanges. Autom Remote Control 80, 1098–1108 (2019). https://doi.org/10.1134/S0005117919060080

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  • DOI: https://doi.org/10.1134/S0005117919060080

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