Description

The increasing complexity and interdependence of the world have elevated the importance of risk management. In addition to making one-time decisions, risk managers are also concerned with the evolution of risk over time. This creates the need for dynamic risk measures that can be used to address problems involving a multi-period setting. One of the key issues of dynamic risk measures is time consistency, i.e. making sure that risk preferences are consistent across different time-periods. In our work we have developed methods for generating dynamic time-consistent approximations of risk-averse stochastic optimization problems.

Matlab, CPLEX

Description

In this work we study the problem of defending a target such as a stadium or large gathering place where multiple paths lead potential attackers to it. In practice, the notion of “layered defense” is commonly used to describe the idea that we have an outer perimeter where we first seek to capture dangerous entities (vehicles, people, cargo), then perhaps a middle perimeter or perimeters where we do the same thing using different methods and perhaps information gathered from the outer perimeter.

Matlab, CPLEX

Description

In this project we consider the problem of reopening a port after it has been shut down because of a natural disaster, terrorist event or domestic dispute. This results in a long queue of ships to be unloaded. The optimal unloading schedule of the ships is formulated with respect to the due dates of the items in their inventory. We also show that the problem of constructing a schedule which meets all due dates is NP-complete.

Matlab, CPLEX

Description

Problems of clustering and classification of high–dimensional data arise in several areas, including genetics and data mining. Distance–based methods for clustering or classification of high–dimensional data often suffer from the unreliability of distances in very high–dimensional spaces. We propose a probabilistic clustering method based on the $\ell_1$–distance that is less sensitive to the high dimensionality. The complexity of the algorithm is linear in the dimension of the data space, and its performance was observed to improve significantly as that dimension increases.

C++, Matlab

Description

The global terrorism threat is especially relevant in the modern era of worldwide flow of goods and people. High density city areas are vulnerable to possible nuclear attacks because of the enormous number of people and the diversity of the products being shipped to the very heart of the city. Any possible extensive network of nuclear sensors that would encompass an entire city, with sensors placed in a grid of reasonably small grid size would have prohibitive cost. An alternative solution would be to use a small number of mobile sensors placed in police cars and taxi cabs. In that case, a number of questions arise: How many taxi and police cars do we need to equip with sensors? How important are sensor specications such as range and probability of error? How much time would it take to detect a mobile or stationary nuclear source? In order shed some light on these issues we have studied the effects of shielding nuclear materials and developed a discrete time computer simulation for urban mobile detection.

Tools

VisualBasic.NET, Matlab

Description

More than a hundred million cargo containers cross international borders every year as a result of the world globalization. In view of the recent political emphasis on security, non-invasive cargo inspection which employs sensors capable of detecting nuclear materials, biological agents and other hazardous shipments has become an issue of great importance. Data generated from different inspection devices are often relied upon to make critical decisions with regard to the nature of the container and the appropriate response mechanism. The process of designing an efficient inspection system must be deliberate and well thought-out, taking into account technological, budget and time constraints. The order in which we apply the sensors, as well as their threshold levels could greatly influence the performance of the inspection system. In our work we developed several algorithms for optimization of sensor networks utilizing both deterministic and radomized inspection strategies.

Matlab, C++

Description

Coding theory is an interdisciplinary field that deals with data transmission in the presence of noise. Error correcting codes(ECCs) are mathematical languages for communication over noisy channels. As such, they find countless applications in the modern world - from correcting the scratches on your CD's to ensuring reliable communication with deep-space satellites. In this project we studied several classes of ECCs and developed new methods and algorithms for the construction of codes with better parameters than previously known. In addition, we also developed the first database for codes over Z4, which can be found at z4codes.net

Tools

MAGMA, Matlab, C++, Asp.NET, MS Access

Description

It is a common practive to use Federal Funds futures prices to estimate the probabilities associated with potential target rates that might be chosen at upcoming FOMC meetings. Using the futures price to recover the ex ante probability associated with an FOMC target rate decision requires several restrictive assumptions, in particular the assumption that the FOMC will only consider two possible target rates in its deliberations. If option prices across several strikes are available, ex ante probabilities can be recovered without resorting to this restrictive assumption. Intuitively, the variation in option prices across the different strikes provides more information than does the single futures price. This additional information allows for the recovery of more than just the ex ante probabilities associated with a single pair of possible FOMC target rate choices. Further, the implied probability density can be computed in an efficient manner. The objective of the project was to design and develop an application which runs on a Bloomberg terminal and computes the probability densities for the outcomes of upcoming FOMC meetings in real time.

Instructor

Professor Chris LaSota