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Consumption-investment problems with transaction costs: Survey and open problems

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  • Abel Cadenillas

Abstract

We present a survey of problems and methods contained in various works on consumption-investment problems with transaction costs in continuous time. The methods are those of optimal stopping, stochastic singular control, and stochastic impulse control. We also describe some open problems in this active area of research. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Abel Cadenillas, 2000. "Consumption-investment problems with transaction costs: Survey and open problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(1), pages 43-68, February.
    • Handle: RePEc:spr:mathme:v:51:y:2000:i:1:p:43-68
    DOI: 10.1007/s001860050002
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    Citations

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    Cited by:

    1. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2016. "A multi-asset investment and consumption problem with transaction costs," Papers 1612.01327, arXiv.org.
    2. Wang, Ting & Young, Virginia R., 2012. "Maximizing the utility of consumption with commutable life annuities," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 352-369.
    3. Stefano Baccarin & Daniele Marazzina, 2014. "Optimal impulse control of a portfolio with a fixed transaction cost," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 355-372, June.
    4. C. Atkinson & C. A. Alexandropoulos, 2006. "Pricing a European Basket Option in the Presence of Proportional Transaction Costs," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(3), pages 191-214.
    5. Luitgard Veraart, 2010. "Optimal Market Making in the Foreign Exchange Market," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(4), pages 359-372.
    6. Luitgard Veraart, 2010. "Optimal investment in the foreign exchange market with proportional transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 631-640.
    7. Yuval Salant & Ron Siegel, 2016. "Reallocation Costs and Efficiency," American Economic Journal: Microeconomics, American Economic Association, vol. 8(1), pages 203-227, February.
    8. Ohnishi, Masamitsu & Tsujimura, Motoh, 2006. "An impulse control of a geometric Brownian motion with quadratic costs," European Journal of Operational Research, Elsevier, vol. 168(2), pages 311-321, January.
    9. Girlich, Hans-Joachim, 2003. "Transaction costs in finance and inventory research," International Journal of Production Economics, Elsevier, vol. 81(1), pages 341-350, January.
    10. Framstad, Nils Chr., 2014. "The Effect of Small Intervention Costs on the Optimal Extraction of Dividends and Renewable Resources in a Jump-Diffusion Model," Memorandum 25/2014, Oslo University, Department of Economics.
    11. Wei Yan, 2017. "Closed-Form Optimal Strategies of Continuous-Time Options with Stochastic Differential Equations," Complexity, Hindawi, vol. 2017, pages 1-11, July.
    12. David Hobson & Yeqi Zhu, 2014. "Multi-asset consumption-investment problems with infinite transaction costs," Papers 1409.8037, arXiv.org.

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