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Portfolio optimisation with strictly positive transaction costs and impulse control

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  • Ralf Korn

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    (FB Mathematik, Johannes-Gutenberg-UniversitÄt Mainz, D-55099 Mainz, Germany)

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    Abstract

    One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a nontrivial asymptotically optimal solution for the problem of exponential utility maximisation.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 2 (1998)
    Issue (Month): 2 ()
    Pages: 85-114

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    Handle: RePEc:spr:finsto:v:2:y:1998:i:2:p:85-114

    Note: received: April 1996; final version received: January 1997
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    Related research

    Keywords: Portfolio optimisation; transaction costs; impulse control; asymptotic analysis.;

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    Cited by:
    1. Peter Diesinger & Holger Kraft & Frank Seifried, 2010. "Asset allocation and liquidity breakdowns: what if your broker does not answer the phone?," Finance and Stochastics, Springer, Springer, vol. 14(3), pages 343-374, September.
    2. Seydel, Roland C., 2009. "Existence and uniqueness of viscosity solutions for QVI associated with impulse control of jump-diffusions," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 119(10), pages 3719-3748, October.
    3. Stefano Baccarin & Daniele Marazzina, 2013. "Portfolio Optimization over a Finite Horizon with Fixed and Proportional Transaction Costs and Liquidity Constraints," Working papers, Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino 017, Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    4. Lakdere Benkherouf & Michael Johnson, 2012. "Optimality of (s, S) policies for jump inventory models," Computational Statistics, Springer, Springer, vol. 76(3), pages 377-393, December.
    5. SCRIMALI, Laura, 2006. "A quasi-variational inequality approach to the financial equilibrium problem," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2006108, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Ren Liu & Johannes Muhle-Karbe & Marko Weber, 2014. "Rebalancing with Linear and Quadratic Costs," Papers 1402.5306, arXiv.org.
    7. Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, Elsevier, vol. 196(1), pages 198-206, July.
    8. Zakamouline, Valeri I., 2006. "European option pricing and hedging with both fixed and proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 30(1), pages 1-25, January.
    9. Yan Dolinsky & Yuri Kifer, 2014. "Risk Minimization in Markets Imposing Minimal Transaction Costs," Papers 1408.3774, arXiv.org.
    10. Andriy Demchuk, 2002. "Portfolio Optimization with Concave Transaction Costs," FAME Research Paper Series, International Center for Financial Asset Management and Engineering rp103, International Center for Financial Asset Management and Engineering.
    11. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2014. "Trading with Small Price Impact," Papers 1402.5304, arXiv.org.
    12. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802, arXiv.org, revised Oct 2013.
    13. Qingshuo Song & G. Yin & Chao Zhu, 2010. "Utility Maximization of an Indivisible Market with Transaction Costs," Papers 1003.2930, arXiv.org.
    14. Cadenillas, Abel & Zapatero, Fernando, 1999. "Optimal Central Bank Intervention in the Foreign Exchange Market," Journal of Economic Theory, Elsevier, Elsevier, vol. 87(1), pages 218-242, July.
    15. S\"oren Christensen & Marc Wittlinger, 2012. "Optimal relaxed portfolio strategies for growth rate maximization problems with transaction costs," Papers 1209.0305, arXiv.org, revised Jun 2013.
    16. Ale\v{s} \v{C}ern\'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy models and the time step equivalent of jumps," Papers 1309.7833, arXiv.org, revised Nov 2013.
    17. Chellathurai, Thamayanthi & Draviam, Thangaraj, 2007. "Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 31(7), pages 2168-2195, July.

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