The Annals of Applied Probability

Singular optimal strategies for investment with transaction costs

Ananda P. N. Weerasinghe

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 8, Number 4 (1998), 1312-1330.

Dates
First available in Project Euclid: 9 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1028903383

Digital Object Identifier
doi:10.1214/aoap/1028903383

Mathematical Reviews number (MathSciNet)
MR1661192

Zentralblatt MATH identifier
0967.93096

Subjects
Primary: 93E20: Optimal stochastic control 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 90A10 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Stochastic optimal control transaction costs local time diffusion processes

Citation

Weerasinghe, Ananda P. N. Singular optimal strategies for investment with transaction costs. Ann. Appl. Probab. 8 (1998), no. 4, 1312--1330. doi:10.1214/aoap/1028903383. https://projecteuclid.org/euclid.aoap/1028903383


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