This review article is intended to collect and summarize many of the results in the field of
optimal execution over the last twenty years. In doing so, we describe the general workings …

We provide two explicit closed-form optimal execution strategies to target volume weighted
average price (VWAP). We do this under very general assumptions about the stochastic …

We develop a high frequency (HF) trading strategy where the HF trader uses her superior
speed to process information and to post limit sell and buy orders. By introducing a …

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

We consider the time interval ${\Delta} $ during which the market trade time-series are
averaged as the key factor of the consumption-based asset-pricing model that causes …

Designing algorithmic trading strategies targeting volume-weighted average price (VWAP)
for long-duration orders is a critical concern for brokers. Traditional rule-based strategies are …

We introduce the price probability measure η (p; t) that defines the mean price p (1; t), mean
square price p (2; t), price volatility σp2 (t) and all price n-th statistical moments p (n; t) as …

We consider the core problems of the conventional value-at-risk (VaR) based on the price
probability determined by frequencies of trades at a price p during an averaging time interval …

The thesis studies algorithmic trading problems for liquidity takers (LTs) and liquidity
providers (LPs) in traditional electronic markets and in decentralised trading platforms that …

Optimal execution, ie, the determination of the most cost-effective way to trade volumes in
continuous trading sessions, has been a topic of interest in the equity trading world for years …