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On the closure in the Emery topology of semimartingale wealth-process sets

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  • Constantinos Kardaras

Abstract

A wealth-process set is abstractly defined to consist of nonnegative c\`{a}dl\`{a}g processes containing a strictly positive semimartingale and satisfying an intuitive re-balancing property. Under the condition of absence of arbitrage of the first kind, it is established that all wealth processes are semimartingales and that the closure of the wealth-process set in the Emery topology contains all "optimal" wealth processes.

Suggested Citation

  • Constantinos Kardaras, 2011. "On the closure in the Emery topology of semimartingale wealth-process sets," Papers 1108.0945, arXiv.org, revised Jul 2013.
  • Handle: RePEc:arx:papers:1108.0945
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    File URL: http://arxiv.org/pdf/1108.0945
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    References listed on IDEAS

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    1. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
    2. Dmitry Kramkov & Mihai S^{{i}}rbu, 2006. "On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets," Papers math/0610224, arXiv.org.
    3. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    4. Kardaras, Constantinos & Platen, Eckhard, 2011. "On the semimartingale property of discounted asset-price processes," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2678-2691, November.
    5. Mathias Beiglbock & Walter Schachermayer & Bezirgen Veliyev, 2010. "A Direct Proof of the Bichteler--Dellacherie Theorem and Connections to Arbitrage," Papers 1004.5559, arXiv.org.
    6. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. M. De Donno & M. Pratelli, 2006. "A theory of stochastic integration for bond markets," Papers math/0602532, arXiv.org.
    8. De Donno, M. & Guasoni, P. & Pratelli, M., 2005. "Super-replication and utility maximization in large financial markets," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 2006-2022, December.
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    Citations

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    Cited by:

    1. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem for Continuous Processes," Post-Print hal-01076062, HAL.
    2. Yuri Kabanov & Constantinos Kardaras & Shiqi Song, 2016. "No arbitrage of the first kind and local martingale numéraires," Finance and Stochastics, Springer, vol. 20(4), pages 1097-1108, October.
    3. Likuan Qin & Vadim Linetsky, 2014. "Long Term Risk: A Martingale Approach," Papers 1411.3078, arXiv.org, revised Oct 2016.
    4. Huy N. Chau & Andrea Cosso & Claudio Fontana & Oleksii Mostovyi, 2015. "Optimal investment with intermediate consumption under no unbounded profit with bounded risk," Papers 1509.01672, arXiv.org, revised Jun 2017.
    5. Constantinos Kardaras & Jan Obloj & Eckhard Platen, 2012. "The numeraire property and long-term growth optimality for drawdown-constrained investments," Papers 1206.2305, arXiv.org, revised Nov 2012.
    6. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2014. "Robust Fundamental Theorem for Continuous Processes," Papers 1410.4962, arXiv.org, revised Jul 2015.
    7. Christa Cuchiero & Josef Teichmann, 2015. "A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing," Finance and Stochastics, Springer, vol. 19(4), pages 743-761, October.
    8. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2017. "Stability for gains from large investors' strategies in M1/J1 topologies," Papers 1701.02167, arXiv.org, revised Jan 2018.
    9. Christa Cuchiero & Irene Klein & Josef Teichmann, 2014. "A new perspective on the fundamental theorem of asset pricing for large financial markets," Papers 1412.7562, arXiv.org, revised Sep 2015.
    10. Oleksii Mostovyi, 2014. "Utility maximization in the large markets," Papers 1403.6175, arXiv.org, revised Oct 2014.

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