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@article{Hobson:2019:10.1111/mafi.12187,
author = {Hobson, D and Tse, ASL and Zhu, Y},
doi = {10.1111/mafi.12187},
journal = {Mathematical Finance},
pages = {483--506},
title = {Optimal consumption and investment under transaction costs},
url = {http://dx.doi.org/10.1111/mafi.12187},
volume = {29},
year = {2019}
}

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TY  - JOUR
AB  - In this paper, we consider the Merton problem in a market with a single risky asset and proportional transaction costs. We give a complete solution of the problem up to the solution of a first-crossing problem for a first-order differential equation. We find that the characteristics of the solution (e.g., well-posedness) can be related to some simple properties of a univariate quadratic whose coefficients are functions of the parameters of the problem. Our solution to the problem via the value function includes expressions for the boundaries of the no-transaction wedge. Using these expressions, we prove a precise condition for when leverage occurs. One new and unexpected result is that when the solution to the Merton problem (without transaction costs) involves a leveraged position, and when transaction costs are large, the location of the boundary at which sales of the risky asset occur is independent of the transaction cost on purchases.
AU  - Hobson,D
AU  - Tse,ASL
AU  - Zhu,Y
DO  - 10.1111/mafi.12187
EP  - 506
PY  - 2019///
SN  - 0960-1627
SP  - 483
TI  - Optimal consumption and investment under transaction costs
T2  - Mathematical Finance
UR  - http://dx.doi.org/10.1111/mafi.12187
VL  - 29
ER  -

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