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

Kardaras, Constantinos and 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 1467-9965

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Identification Number: 10.1111/mafi.12081

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
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HG Finance
Q Science > QA Mathematics
Sets: Departments > Statistics
Date Deposited: 11 Nov 2014 11:22
Last Modified: 05 Apr 2017 13:51
Funders: 2011 Bruti-Liberati Fellowship at University of Technology, Sydney
URI: http://eprints.lse.ac.uk/id/eprint/60132

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