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The Deterministic Optimal Liquidation Problem

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Control Systems and Mathematical Methods in Economics

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 687))

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Abstract

A one-dimensional free terminal time optimal control problem stemming from mathematical finance is studied. To find the optimal solution and prove its optimality the standard maximum principle procedure including Arrow’s sufficiency theorem is combined with specific properties of the problem. Certain unexpected features of the solution are pointed out and discussed.

Dedicated to Vladimir Veliov on the occasion of his 65th birthday.

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Notes

  1. 1.

    Because there is no need of the assumption ρ > 0 in the deterministic problem, we ignore it in the sequel.

References

  • R. Almgren, N. Chriss, Optimal execution of portfolio transactions. J. Risk 3, 5–39 (2000)

    Article  Google Scholar 

  • P. Brunovský, A. Černý, M. Winkler, A singular differential equation stemming from am optimal control problem in financial economics. Appl. Math. Optim. 68, 255–274 (2013)

    Article  Google Scholar 

  • P. Brunovský, A. Černý, J. Komadel, Optimal trade execution under endogenou pressure to liquidate: theory and numerical solutions. Eur. J. Oper. Res. 264, 1159–1171 (2018)

    Article  Google Scholar 

  • A. Černý, Current crises: introduction of spot speculators. Int. J. Fin. Econ. 4, 75–90 (1999)

    Article  Google Scholar 

  • G. Feichtinger, R.F. Hartl, P.M. Kort, V.M. Veliov, Anticiaptiaon effects of technological progress on capital accumulation: a vintage capital approach. J. Econ. Theory 126, 143–164 (2006)

    Article  Google Scholar 

  • A. Seierstad, K. Sydsaeter, Optimal Control Theory with Economic Applications, 2nd edn. (Elsevier, North-Holland, 1993)

    Google Scholar 

  • P.S. Sethi, G.T. Thompson, Optimal Control Theory, 2nd edn. (Springer, Berlin, 2006)

    Google Scholar 

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Acknowledgements

The authors are thankful to the anonymous referee for enlightening comments. Research of the second author has been supported by VEGA Grants 1/0780/15 and 01/0062/18.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Comenius University in Bratislava, Bratislava, Slovakia

    Pavol Brunovský, Margaréta Halická & Mario Mitas

Authors
  1. Pavol Brunovský
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  2. Margaréta Halická
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  3. Mario Mitas
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Corresponding author

Correspondence to Pavol Brunovský .

Editor information

Editors and Affiliations

  1. Operations Research and Control Systems, Vienna University of Technology , Vienna, Austria

    Gustav Feichtinger

  2. Operations Research and Control Systems, Vienna University of Technology, Vienna, Austria

    Raimund M. Kovacevic

  3. Operations Research and Control Systems, Vienna University of Technology, Vienna, Austria

    Gernot Tragler

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Brunovský, P., Halická, M., Mitas, M. (2018). The Deterministic Optimal Liquidation Problem. In: Feichtinger, G., Kovacevic, R., Tragler, G. (eds) Control Systems and Mathematical Methods in Economics. Lecture Notes in Economics and Mathematical Systems, vol 687. Springer, Cham. https://doi.org/10.1007/978-3-319-75169-6_13

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