2012/06/11 by Constantinos Kardaras, Kardaras, Constantinos, Jan Obłój +3
Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Portfolio Management (q-fin.PM) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1206.2305
openalex publication_date 2012/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the portfolio choice problem for a long-run investor in a general\ncontinuous semimartingale model. We suggest to use path-wise growth optimality\nas the decision criterion and encode preferences through restrictions on the\nclass of admissible wealth processes. Specifically, the investor is only\ninterested in strategies which satisfy a given linear drawdown constraint. The\npaper introduces the numeraire property through the notion of expected relative\nreturn and shows that drawdown-constrained strategies with the numeraire\nproperty exist and are unique, but may depend on the financial planning\nhorizon. However, when sampled at the times of its maximum and asymptotically\nas the time-horizon becomes distant, the drawdown-constrained numeraire\nportfolio is given explicitly through a model-independent transformation of the\nunconstrained numeraire portfolio. Further, it is established that the\nasymptotically growth-optimal strategy is obtained as limit of numeraire\nstrategies on finite horizons.\n