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

Constantinos Kardaras, Jan Obłój and Eckhard Platen ()

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: Drawdown constraints; numéraire property; asymptotic growth; portfolio risk management (search for similar items in EconPapers)
JEL-codes: C1 F3 G3 (search for similar items in EconPapers)
Date: 2017-01-01
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Citations: View citations in EconPapers (3)

Published in Mathematical Finance, 1, January, 2017, 27(1), pp. 68-95. ISSN: 0960-1627

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http://eprints.lse.ac.uk/60132/ Open access version. (application/pdf)

Related works:
Journal Article: THE NUMÉRAIRE PROPERTY AND LONG-TERM GROWTH OPTIMALITY FOR DRAWDOWN-CONSTRAINED INVESTMENTS (2017)
Working Paper: The numeraire property and long-term growth optimality for drawdown-constrained investments (2012)
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