We consider the finite-time optimal portfolio liquidation problem for a von Neumann-Morgenstern investor with constant absolute risk aversion (CARA). As underlying market impact model, we use the continuous-time liquidity model of Almgren and Chriss (2000). We show that the expected utility of sales revenues, taken over a large class of adapted strategies, is maximized by a deterministic strategy, which is explicitly given in terms of an analytic formula. The proof relies on the observation that the corresponding value function solves a degenerate Hamilton-Jacobi-Bellman equation with singular initial condition.

We consider the problem of portfolio liquidation with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact. For a simple linear cost model, we explicitly construct the efficient frontier in the space of time-dependent liquidation strategies, which have minimum expected cost for a given level of uncertainty. We consider the risk-reward tradeoff both from the point of view of classic mean-variance optimization, and from the standpoint of Value at Risk. This analysis leads to general insights into optimal portfolio trading, and to several applications including a definition of liquidity-adjusted value at risk.

We consider the infinite-horizon optimal portfolio liquidation problem for a von Neumann-Morgenstern investor in the liquidity model of Almgren (2003). Using a stochastic control approach, we characterize the value function and the optimal strategy as classical solutions of nonlinear parabolic partial differential equations. We furthermore analyze the sensitivities of the value function and the optimal strategy with respect to the various model parameters. In particular, we find that the optimal strategy is aggressive or passive in-the-money, respectively, if and only if the utility function displays increasing or decreasing risk aversion. Surprisingly, only few further monotonicity relations exist with respect to the other parameters. We point out in particular that the speed by which the remaining asset position is sold can be decreasing in the size of the position but increasing in the liquidity price impact.

Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handboo

We develop a partial equilibrium model to investigate the problem of optimal liquidation over a finite or infinite time horizon for an investor with large holdings in a risky asset. The imperfect liquidity in the market for the asset leads to a nonlinear path dependent feedback on the underlying asset price process due to the large investor's trades and his holdings in the asset. We use probabilistic techniques to prove verification and existence results for optimal liquidation policies for the utility-maximizing investor under broad assumptions. In particular, our results imply the existence of optimal policies if the investor has power utility functions. We provide analytical expressions for the optimal policy when the large investor has logarithmic preferences. We use these results to characterize the quot;liquidity discountquot;; a measure of the liquidity risk of the large investor's position in the risky asset.

This book is devoted to mathematical models for execution problems in finance. The main goal is to present a general framework (inspired from the Almgren-Chriss approach) for optimal execution problems, and then to use it in a wide range of areas. The book covers applications to the different types of execution proposed within the brokerage industry. It also presents applications to block trade pricing, to portfolio management and to option pricing.

Artificial intelligence (AI) has grown in presence in asset management and has revolutionized the sector in many ways. It has improved portfolio management, trading, and risk management practices by increasing efficiency, accuracy, and compliance. In particular, AI techniques help construct portfolios based on more accurate risk and return forecasts and more complex constraints. Trading algorithms use AI to devise novel trading signals and execute trades with lower transaction costs. AI also improves risk modeling and forecasting by generating insights from new data sources. Finally, robo-advisors owe a large part of their success to AI techniques. Yet the use of AI can also create new risks and challenges, such as those resulting from model opacity, complexity, and reliance on data integrity.

This book is essential in understanding, investing and risk managing the holy grail of investments - structured products. The book begins by introducing structured products by way of a basic guide so that readers will be able to understand a payoff graphic, read a termsheet or assess a payoff formula, before moving on to the key asset classes and their peculiarities. Readers will then move on to the more advanced subjects such as structured products construction and behaviour during their lifetime. It also explains how to avoid important pitfalls in products across all asset classes, pitfalls that have led to huge losses over recent years, including detailed coverage of counterparty risk, the fall of Lehman Brothers and other key aspects of the financial crisis related to structured products. The second part of the book presents an original approach to implementing structured products in a portfolio. Key features include: A comprehensive list of factors an investor needs to take into consideration before investing. This makes it a great help to any buyer of structured products; Unbiased advice on product investments across several asset classes: equities, fixed income, foreign exchange and commodities; Guidance on how to implement structured products in a portfolio context; A comprehensive questionnaire that will help investors to define their own investment preferences, allowing for a greater precision when facing investment decisions; An original approach determining the typical distribution of returns for major product types, essential for product classification and optimal portfolio implementation purposes; Written in a fresh, clear and understandable style, with many figures illustrating the products and very little mathematics. This book will enable you to better comprehend the use of structured products in everyday banking, quickly analyzing a product, assessing which of your clients it suits, and recognizing its major pitfalls. You will be able to see the added value versus the cost of a product and if the payoff is compatible with the market expectations.

The first part of this book discusses institutions and mechanisms of algorithmic trading, market microstructure, high-frequency data and stylized facts, time and event aggregation, order book dynamics, trading strategies and algorithms, transaction costs, market impact and execution strategies, risk analysis, and management. The second part covers market impact models, network models, multi-asset trading, machine learning techniques, and nonlinear filtering. The third part discusses electronic market making, liquidity, systemic risk, recent developments and debates on the subject.

Crescenzi makes frequent appearances on CNBC, Bloomberg, and NBC's “Wall Street Journal Report with Maria Bartiromo” and he has acted as advisor to members of the White House The author is a featured columnist for thestreet.com's” Real Money” and has a strong professional following The book covers all major instruments and investment choices