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We revisit the optimal investment and consumption problem with proportionaltransaction costs. We prove that both the value function and the slopes of thelines demarcating the no-trading region are analytic functions of cube root ofthe transaction cost parameter. Also, we can explicitly calculate thecoefficients of the fractional power series expansions of the value functionand the no-trading region.

Asymptotic analysis for Merton's problem with transaction costs in power utility case