Abstract
We consider the optimal consumption and investment with transaction costs on multiple assets, where the prices of risky assets jointly follow a multi-dimensional geometric Brownian motion. We characterize the optimal investment strategy and in particular prove by rigorous mathematical analysis that the trading region has the shape that is very much needed for well defining the trading strategy, e.g., the no-trading region has distinct corners. In contrast, the existing literature is restricted to either single risky asset or multiple uncorrelated risky assets.
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