The dual optimizer for the growth-optimal portfolio under transaction costs
We consider the maximization of the long-term growth rate in the Black-Scholes model under proportional transaction costs as in Taksar, Klass and Assaf [Math. Oper. Res. 13, 1988]. Similarly as in Kallsen and Muhle-Karbe [Ann. Appl. Probab., 20, 2010] for optimal consumption over an infinite horizon, we tackle this problem by determining a shadow price, which is the solution of the dual problem. It can be calculated explicitly up to determining the root of a deterministic function. This in turn allows to explicitly compute fractional Taylor expansions, both for the no-trade region of the optimal strategy and for the optimal growth rate.
Year of publication: |
2010-05
|
---|---|
Authors: | Gerhold, Stefan ; Muhle-Karbe, Johannes ; Schachermayer, Walter |
Institutions: | arXiv.org |
Saved in:
freely available
Saved in favorites
Similar items by person
-
Transaction Costs, Trading Volume, and the Liquidity Premium
Gerhold, Stefan, (2011)
-
Asymptotics and Duality for the Davis and Norman Problem
Gerhold, Stefan, (2010)
-
Transaction Costs, Shadow Prices, and Duality in Discrete Time
Czichowsky, Christoph, (2012)
- More ...