In this review article, we present recent work on the regularity of dynamical market impact
models and their associated optimal order execution strategies. In particular, we address the …

With an alternative choice of risk criterion, we solve the HJB equation explicitly to find a
closed-form solution for the optimal trade execution strategy in the Almgren–Chriss …

We propose the use of a mean quadratic variation criteria to determine an optimal trading
strategy in the presence of price impact. We derive the Hamilton Jacobi Bellman (HJB) …

We consider the problem of mean-variance optimal agency execution strategies, when the
market liquidity and volatility vary randomly in time. Under specific assumptions for the …

The viability of a market impact model is usually considered to be equivalent to the absence
of price manipulation strategies. By analyzing a model with linear instantaneous, transient …

We analyze the existence of price manipulation and optimal trade execution strategies in a
model for an electronic limit order book with nonlinear price impact and exponential …

The classical literature on optimal liquidation, rooted in Almgren–Chriss models, tackles the
optimal liquidation problem using a trade‐off between market impact and price risk. It …

In recent years, academics, regulators, and market practitioners have increasingly
addressed liquidity issues. Among the numerous problems addressed, the optimal …

Optimal execution is an important problem faced by any trader. Most solutions are based on
the assumption of constant market impact, while liquidity is known to be dynamic. Moreover …

This paper considers the pricing and hedging of a call option when liquidity matters, that is,
either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the …