Mathematical programming methods of pattern classification

Mathematical programming methods of pattern classificatio

Anomalous price impact and the critical nature of liquidity in financial markets

We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {\it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This naturally accounts for two striking stylized facts: first, large metaorders have to be fragmented in order to be digested by the liquidity funnel, leading to long-memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of linear response and a diverging impact of small orders, explaining the "square-root" impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients.Comment: 16 pages, 7 figure

How many independent bets are there?

The benefits of portfolio diversification is a central tenet implicit to modern financial theory and practice. Linked to diversification is the notion of breadth. Breadth is correctly thought of as the number of in- dependent bets available to an investor. Conventionally applications us- ing breadth frequently assume only the number of separate bets. There may be a large discrepancy between these two interpretations. We uti- lize a simple singular-value decomposition (SVD) and the Keiser-Gutman stopping criterion to select the integer-valued effective dimensionality of the correlation matrix of returns. In an emerging market such as South African we document an estimated breadth that is considerably lower than anticipated. This lack of diversification may be because of market concentration, exposure to the global commodity cycle and local currency volatility. We discuss some practical extensions to a more statistically correct interpretation of market breadth, and its theoretical implications for both global and domestic investors.Comment: Less technical rewrite. 12 Pages, 6 Figures (.eps

A simple scheme for allocating capital in a foreign exchange proprietary trading firm

We present a model of capital allocation in a foreign exchange proprietary trading firm. The owner allocates capital to individual traders, who operate within strict risk limits. Traders specialize in individual currencies, but are given discretion over their choice of trading rule. The owner provides the simple formula that determines position sizes – a formula that does not require estimation of the firm-level covariance matrix. We provide supporting empirical evidence of excess risk-adjusted returns to the firm-level portfolio, and we discuss a modification of the model in which the owner dictates the choice of trading rule

Algorithms for flows over time with scheduling costs

Flows over time have received substantial attention from both an optimization and (more recently) a game-theoretic perspective. In this model, each arc has an associated delay for traversing the arc, and a bound on the rate of flow entering the arc; flows are time-varying. We consider a setting which is very standard within the transportation economic literature, but has received little attention from an algorithmic perspective. The flow consists of users who are able to choose their route but also their departure time, and who desire to arrive at their destination at a particular time, incurring a scheduling cost if they arrive earlier or later. The total cost of a user is then a combination of the time they spend commuting, and the scheduling cost they incur. We present a combinatorial algorithm for the natural optimization problem, that of minimizing the average total cost of all users (i.e., maximizing the social welfare). Based on this, we also show how to set tolls so that this optimal flow is induced as an equilibrium of the underlying game

Can modeling of HIV treatment processes improve outcomes? Capitalizing on an operations research approach to the global pandemic

<p>Abstract</p> <p>Background</p> <p>Mathematical modeling has been applied to a range of policy-level decisions on resource allocation for HIV care and treatment. We describe the application of classic operations research (OR) techniques to address logistical and resource management challenges in HIV treatment scale-up activities in resource-limited countries.</p> <p>Methods</p> <p>We review and categorize several of the major logistical and operational problems encountered over the last decade in the global scale-up of HIV care and antiretroviral treatment for people with AIDS. While there are unique features of HIV care and treatment that pose significant challenges to effective modeling and service improvement, we identify several analogous OR-based solutions that have been developed in the service, industrial, and health sectors.</p> <p>Results</p> <p>HIV treatment scale-up includes many processes that are amenable to mathematical and simulation modeling, including forecasting future demand for services; locating and sizing facilities for maximal efficiency; and determining optimal staffing levels at clinical centers. Optimization of clinical and logistical processes through modeling may improve outcomes, but successful OR-based interventions will require contextualization of response strategies, including appreciation of both existing health care systems and limitations in local health workforces.</p> <p>Conclusion</p> <p>The modeling techniques developed in the engineering field of operations research have wide potential application to the variety of logistical problems encountered in HIV treatment scale-up in resource-limited settings. Increasing the number of cross-disciplinary collaborations between engineering and public health will help speed the appropriate development and application of these tools.</p