The numéraire property and long-term growth optimality for drawdown-constrained investments

Kardaras, Constantinos ORCID: 0000-0001-6903-4506, Obłój, Jan and Platen, Eckhard (2017) The numéraire property and long-term growth optimality for drawdown-constrained investments. Mathematical Finance, 27 (1). pp. 68-95. ISSN 0960-1627

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Abstract

We consider the portfolio choice problem for a long-run investor in a general continuous semimartingale model. We combine the decision criterion of pathwise growth optimality with a flexible specification of attitude towards risk, encoded by a linear drawdown constraint imposed on admissible wealth processes. We define the constrained numraire property through the notion of expected relative return and prove that drawdown-constrained numéraire portfolio exists and is unique, but may depend on the investment horizon. However, when sampled at the times of its maximum and asymptotically as the time-horizon becomes distant, the drawdown-constrained numéraire portfolio is given explicitly through a model-independent transformation of the unconstrained numéraire portfolio. The asymptotically growth-optimal strategy is obtained as limit of numéraire strategies on finite horizons.

Item Type:	Article
Official URL:	http://onlinelibrary.wiley.com/journal/10.1111/%28...
Additional Information:	© 2014 John Wiley & Sons Ltd
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HG Finance Q Science > QA Mathematics
Date Deposited:	11 Nov 2014 11:22
Last Modified:	01 Oct 2024 03:44
Funders:	2011 Bruti-Liberati Fellowship at University of Technology, Sydney
URI:	http://eprints.lse.ac.uk/id/eprint/60132

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