Worst-case portfolio optimization with proportional transaction costs

Belak, Christoph, Menkens, Olaf and Sass, Jorn
(2015)
Worst-case portfolio optimization with proportional transaction costs.
Stochastics An International Journal of Probability and Stochastic Processes, 87
(4).
pp. 623-663.
ISSN 1744-2516

We study optimal asset allocation in a crash-threatened financial market with proportional transaction costs. The market is assumed to be in either a normal state, in which the risky asset follows a geometric Brownian motion, or in a crash state, in which the price of the risky asset can suddenly drop by a certain relative amount. We only assume the maximum number and the maximum relative size of the crashes to be given and do not make any assumptions about their distributions. For every investment strategy, we identify the worst-case scenario in the sense that the expected utility of terminal wealth is minimized. The objective is then to determine the investment strategy which yields the highest expected utility in its worst-case scenario.
We solve the problem for utility functions with constant relative risk aversion using a stochastic control approach. We characterize the value function as the unique viscosity solution of a second-order nonlinear partial differential equation. The optimal strategies are characterized by time-dependent free boundaries which we compute numerically. The numerical examples suggest that it is not optimal to invest any wealth in the risky asset close to the investment horizon, while a long position in the risky asset is optimal if the remaining investment period is sufficiently large.

This is an electronic version of an article published in 'Stochastics An International Journal of Probability and Stochastic Processes', available online at http://dx.doi.org/10.1080/17442508.2014.991325

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This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License

Funders:

Science Foundation Ireland (SFI), Deutsche Forschungsgemeinschaft (DFG)

ID Code:

20853

Deposited On:

07 Oct 2015 10:16 by
Olaf Menkens
. Last Modified 19 Jul 2018 15:07

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