Ergodic robust maximization of asymptotic growth

Constantinos Kardaras and Scott Robertson

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

Abstract: We consider the problem of robustly maximizing the growth rate of investor wealth in the presence of model uncertainty. Possible models are all those under which the assets’ region E and instantaneous covariation c are known, and where the assets are stable with an exogenously given limiting density p, in that their occupancy time measures converge to a law governed by p. This latter assumption is motivated by the observed stability of ranked relative market capitalizations for equity markets. We seek to identify the robust optimal growth rate, as well as a trading strategy which achieves this rate in all models. Under minimal assumptions upon (E, c, p), which in particular allow for an arbitrary number of assets, we identify the robust growth rate with the Donsker–Varadhan rate function from occupancy time large deviations theory. We also explicitly obtain the optimal trading strategy. We apply our results to the case of drift uncertainty for ranked relative market capitalizations. Here, assuming regularity under symmetrization for the covariance and limiting density of the ranked capitalizations, we explicitly identify the robust optimal trading strategy.

Keywords: long horizon; model uncertainty; robust growth; schastic portfolio theory (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 33 pages
Date: 2021-08-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Annals of Applied Probability, 1, August, 2021, 31(4), pp. 1787-1819. ISSN: 1050-5164

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:121039

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