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In a market with priceimpact proportional to a power of the order flow, we derive optimal trading policies and their implied welfare for longterm investors with constant relative risk aversion, who trade one safe asset and one risky asset that follows geometric Brownian motion. These quantities admit asymptotic explicit formulas up to a structural constant that depends only on the priceimpact exponent. Trading rates are finite as with linear impact, but they are lower near the target portfolio, and higher away from the target. The model nests the squareroot impact law and, as extreme cases, linear impact and proportional transaction costs.
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