We study an investment decision problem for an investor who has
available a risk-free asset (such as a bank account) and a chosen risky asset.
It is assumed that the interest rate for the risk-free asset is zero. The
amount invested in the risky asset is given by an Itô process with
infinitesimal parameters $\mu (\cdot)$ and $\sigma (\cdot)$, which come from a
control set. This control set depends on the investor's wealth in the risky
asset. The wealth can be transferred between the two assets and there are
charges on all transactions equal to a fixed percentage of the amount
transacted. The investor's financial goal is to achieve a total wealth of $a
> 0$. The objective is to find an optimal strategy to maximize the
probability of reaching a total wealth a before bankruptcy. Under
certain conditions on the control sets, an optimal strategy is found that
consists of an optimal choice of a risky asset and an optimal choice for the
allocation of wealth (buying and selling policies) between the two assets.
Publié le : 1998-11-14
Classification:
Stochastic optimal control,
transaction costs,
local time,
diffusion processes,
93E20,
60G40,
90A10,
60H10
@article{1028903383,
author = {Weerasinghe, Ananda P. N.},
title = {Singular optimal strategies for investment with transaction
costs},
journal = {Ann. Appl. Probab.},
volume = {8},
number = {1},
year = {1998},
pages = { 1312-1330},
language = {en},
url = {http://dml.mathdoc.fr/item/1028903383}
}
Weerasinghe, Ananda P. N. Singular optimal strategies for investment with transaction
costs. Ann. Appl. Probab., Tome 8 (1998) no. 1, pp. 1312-1330. http://gdmltest.u-ga.fr/item/1028903383/