The numéraire property and long-term growth optimality for drawdown-constrained investments
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.
|Date of creation:||Jan 2017|
|Publication status:||Published in Mathematical Finance, January, 2017, 27(1), pp. 68-95. ISSN: 1467-9965|
|Contact details of provider:|| Postal: LSE Library Portugal Street London, WC2A 2HD, U.K.|
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