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.
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Parts of the paper were written during the author's visit at the Isaac Newton Institute for Mathematical Science in Cambridge, UK. The revised version was prepared when the author was on sabbatical at the Dept. of Electrical and Electronic Engineering, Imperial College of Science and Technology, London. The author appreciates both these invitations very much.
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Korn, R. Value preserving portfolio strategies in continuous-time models. Mathematical Methods of Operations Research 45, 1–43 (1997). https://doi.org/10.1007/BF01194246
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DOI: https://doi.org/10.1007/BF01194246