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Value preserving portfolio strategies in continuous-time models

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  • Ralf Korn

Abstract

We present a new approach for continuous-time portfolio strategies that relies on the principle of value preservation. This principle was developed by Hellwig (1987) for general economic decision and pricing models. The key idea is that an investor should try to consume only so much of his portfolio return that the future ability of the portfolio should be kept constant over time. This ensures that the portfolio will be a long lasting source of income. We define a continuous-time market setting to apply the idea of Hellwig to securities markets with continuous trading and examine existence (and uniqueness) of value-preserving strategies in some widely used market models. Further, we discuss the existence of such strategies in markets with constraints and incompleteness. Copyright Physica-Verlag 1997

Suggested Citation

  • Ralf Korn, 1997. "Value preserving portfolio strategies in continuous-time models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(1), pages 1-43, February.
    • Handle: RePEc:spr:mathme:v:45:y:1997:i:1:p:1-43
    DOI: 10.1007/BF01194246
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    References listed on IDEAS

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    1. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    4. Hua He & Neil D. Pearson, 1991. "Consumption and Portfolio Policies With Incomplete Markets and Short‐Sale Constraints: the Finite‐Dimensional Case1," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 1-10, July.
    5. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    6. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
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    Cited by:

    1. Klaus Hellwig, 2002. "Value management," Quantitative Finance, Taylor & Francis Journals, vol. 2(2), pages 133-138.
    2. Hellwig, Klaus, 2004. "Portfolio selection subject to growth objectives," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 2119-2128, September.
    3. Hellwig, Klaus, 2007. "The creation of wealth," Finance Research Letters, Elsevier, vol. 4(3), pages 172-178, September.
    4. Ralf Korn, 1998. "Value preserving portfolio strategies and the minimal martingale measure," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(2), pages 169-179, June.

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