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On value preserving and growth optimal portfolios

Author

Listed:
  • Ralf Korn
  • Manfred Schäl

Abstract

In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will turn out that these concepts are all associated with a unique martingale measure which agrees with the minimal martingale measure only for complete markets. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • Ralf Korn & Manfred Schäl, 1999. "On value preserving and growth optimal portfolios," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 189-218, October.
    • Handle: RePEc:spr:mathme:v:50:y:1999:i:2:p:189-218
    DOI: 10.1007/s001860050095
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    Citations

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    Cited by:

    1. Eckhard Platen & Jason West, 2004. "A Fair Pricing Approach to Weather Derivatives," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 23-53, March.
    2. Hardy Hulley & Shane Miller & Eckhard Platen, 2005. "Benchmarking and Fair Pricing Applied to Two Market Models," Research Paper Series 155, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Lagerkvist, Carl Johan & Gregory, Mark & Olson, Kent D., 2003. "Enhancing The Competitiveness And Risk-Efficiency Of Farm Assets Through Holding Farm/Financial Asset And Off-Farm Income Portfolios," 2003 Annual meeting, July 27-30, Montreal, Canada 22125, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    4. Eckhard Platen, 2004. "A Benchmark Framework for Risk Management," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 305-335, World Scientific Publishing Co. Pte. Ltd..
    5. Fontana, Claudio & Runggaldier, Wolfgang J., 2021. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 66-80.
    6. Hellwig, Klaus, 2004. "Portfolio selection subject to growth objectives," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 2119-2128, September.
    7. Laurence Carassus & Miklós Rásonyi, 2007. "Optimal Strategies and Utility-Based Prices Converge When Agents’ Preferences Do," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 102-117, February.
    8. Morten Christensen & Eckhard Platen, 2004. "A General Benchmark Model for Stochastic Jump Sizes," Research Paper Series 139, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2009, January-A.
    10. Jörn Sass & Manfred Schäl, 2014. "Numeraire portfolios and utility-based price systems under proportional transaction costs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 195-234, October.
    11. Eckhard Platen & Wolfgang Runggaldier, 2004. "A Benchmark Approach to Filtering in Finance," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 79-105, March.
    12. Hellwig, Klaus, 2007. "The creation of wealth," Finance Research Letters, Elsevier, vol. 4(3), pages 172-178, September.
    13. Jan Natolski & Ralf Werner, 2017. "Mathematical Analysis of Replication by Cash Flow Matching," Risks, MDPI, vol. 5(1), pages 1-15, February.
    14. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, July-Dece.
    15. Eckhard Platen, 2004. "Capital Asset Pricing for Markets with Intensity Based Jumps," Research Paper Series 143, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Laurence Carassus & Miklós Rásonyi, 2006. "Convergence of Utility Indifference Prices to the Superreplication Price," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 145-154, August.
    17. Hellwig, Klaus, 2005. "Sustainability revisited," Economics Letters, Elsevier, vol. 87(2), pages 193-197, May.
    18. Ralf Korn & Frank Oertel & Manfred Schäl, 2003. "Notes and Comments: The numeraire portfolio in financial markets modeled by a multi-dimensional jump diffusion process," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 26(2), pages 153-166, November.
    19. Claudio Fontana & Wolfgang J. Runggaldier, 2020. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Papers 2006.15563, arXiv.org, revised Sep 2020.
    20. Klaus Hellwig, 2002. "Value management," Quantitative Finance, Taylor & Francis Journals, vol. 2(2), pages 133-138.
    21. Klaus Hellwig, 2005. "Portfolio Selection with Little Information about the Future," Annals of Economics and Finance, Society for AEF, vol. 6(2), pages 331-335, November.

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