# Periodic strategies in optimal execution with multiplicative price impact

## TL;DR

This paper investigates optimal trading strategies considering multiplicative price impacts, modeling decision times with a Poisson process, and proves that the optimal approach has a barrier structure based on remaining shares and asset price level.

## Contribution

It introduces a novel model for optimal execution with multiplicative price impact and characterizes the optimal strategy as a barrier policy depending on shares and price.

## Key findings

- Optimal strategy has a barrier form.
- Strategy depends only on remaining shares and asset price.
- Expected net gains are maximized under this policy.

## Abstract

In this work we study the optimal execution problem with multiplicative price impact in algorithm trading, when an agent holds an initial position of shares of a financial asset. The inter-selling-decision times are modelled by the arrival times of a Poisson process. The criterion to be optimised consists in maximising the expected net present value of 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 asset price.