We study the uniqueness of viscosity solutions of a Hamilton--Jacobi--Bellman equation which arises in a portfolio optimization problem in which an investor maximizes expected utility of terminal wealth in the presence of proportional transaction costs. Our main contribution is that the comparison theorem can be applied to prove the uniqueness of the value function in the portfolio optimization problem for logarithmic and power utility.
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Belak et al. (2015) studied this question.
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