# Mathematical Finance

## Periodic strategies in optimal execution with multiplicative price impact

### Early View

Abstract We study the optimal execution problem with multiplicative price impact in algorithmic trading, when an agent holds an initial position of shares of a financial asset. The interselling decision times are modeled by the arrival times of a Poisson process. The criterion to be optimized consists in maximizing the expected net present value of the gains of the agent, and it is proved that an optimal strategy has a barrier form, depending only on the number of shares left and the level of the asset price.

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