Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model

Journal article

A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a drawdown constraint, as in the original setup of Grossman and Zhou (1993). We work in an abstract semimartingale financial market model with a general class of utility functions and drawdown constraints. We solve the problem by showing that it is in fact equivalent to an unconstrained problem with a suitably modified utility function. Both the value function and the optimal investment policy for the drawdown problem are given explicitly in terms of their counterparts in the unconstrained problem.

Authors: Cherny, V; Obloj, J

• Publication status: Published
• Journal: Finance and Stochastics
• Volume: 17
• Issue: 4
• Pages: 771-800
• Publication date: 2011-10-28
• DOI: 10.1007/s00780-013-0209-4
• EISSN: 1432-1122
• ISSN: 0949-2984
• Language: English
• Keywords: q-fin.PM; 91G10, 60G44, 60G17