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November 1998 Singular optimal strategies for investment with transaction costs
Ananda P. N. Weerasinghe
Ann. Appl. Probab. 8(4): 1312-1330 (November 1998). DOI: 10.1214/aoap/1028903383


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.


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Ananda P. N. Weerasinghe. "Singular optimal strategies for investment with transaction costs." Ann. Appl. Probab. 8 (4) 1312 - 1330, November 1998.


Published: November 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0967.93096
MathSciNet: MR1661192
Digital Object Identifier: 10.1214/aoap/1028903383

Primary: 60G40 , 93E20
Secondary: 60H10 , 90A10

Keywords: Diffusion processes , Local time , stochastic optimal control , Transaction costs

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.8 • No. 4 • November 1998
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