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Optimal Control Problems with Disorder

  • Control in Technical Systems
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Abstract

We consider a generalization of processes with disorder, namely processes with a vector disorder. For these problems, we consider a class of optimal control problems that do not detect the disorder. We propose a computational method for solving control problems on a finite time interval and with an objective functional defined at the end of the interval, based on the use of the martingale technique. We consider a computational experiment for a model with two barriers and two stopping times.

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References

  1. Shiryaev, A., Quickest Detection Problems in the Technical Analysis of the Financial Data, in Mathematical Finance, Geman, H., Madan, D., Pliska, S., and Vorst, T., Eds., New York: Springer, 2000, pp. 487–521.

    Google Scholar 

  2. Gapeev, P.V. and Peskir, G., The Wiener Disorder Problem with Finite Horizon, Stoch. Proc. Appl., 2006, vol. 116, no. 12, pp. 1770–1791.

    Article  MathSciNet  MATH  Google Scholar 

  3. Truonga, C., Oudrec, L., and Vayatisa, N., A Review of Change Point Detection Methods, arXiv: 1801.00718v1 [cs.CE], Jan 2, 2018.

    Google Scholar 

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

    Google Scholar 

  5. Fel’mer, G. and Shid, A., Stokhasticheskie Finansy (Stochastic Finance), Moscow: MTsNMO, 2008.

    Google Scholar 

  6. Mel’nikov, A.V., Volkov, S.N., and Nechaev, M.L., Matematika finansovykh obyazatel’stv (Mathematics of Financial Obligations), Moscow: Vysshaya Shkola Ekonomiki, 2001.

    Google Scholar 

  7. Rudloff, B., A Generalized Neyman-Pearson Lemma for Hedge Problems in Incomplete Markets, Proc. Workshop “Stochastic Analysis,” 27.09.2004–29.09.2004, pp. 241–249.

  8. Beliavsky, G. and Danilova, N., About (B.S)-Market Model with Stochastic Switching of Parameters, Proc. Int. Conf. Advanced Finance and Stochastics, Moscow, June 24–28, 2013.

    Google Scholar 

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Acknowledgments

This work was financially supported by the Russian Science Foundation, project no. 17-19-01038.

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Authors and Affiliations

  1. Southern Federal University, Rostov-on-Don, Russia

    G. I. Belyavskii, N. V. Danilova & I. A. Zemlyakova

  2. Vorovich Institute of Mathematics, Mechanics, and Computer Science, Rostov-on-Don, Russia

    G. I. Belyavskii, N. V. Danilova & I. A. Zemlyakova

Authors
  1. G. I. Belyavskii
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  2. N. V. Danilova
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  3. I. A. Zemlyakova
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Corresponding authors

Correspondence to G. I. Belyavskii, N. V. Danilova or I. A. Zemlyakova.

Additional information

Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 8, pp. 64–75.

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Belyavskii, G.I., Danilova, N.V. & Zemlyakova, I.A. Optimal Control Problems with Disorder. Autom Remote Control 80, 1419–1427 (2019). https://doi.org/10.1134/S0005117919080046

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  • DOI: https://doi.org/10.1134/S0005117919080046

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