Parallel Multivariate Polynomial Multiplication and Division

In this internship, the team proposes to develop high performance sequential and parallel algorithms for multiplication and division of multivariate polynomials. They propose to use a recursive data structure. One of the possible advantages of a recursive data structure is that we can also see how to parallelize polynomial division. Potentially high level algorithms such as computing polynomial GCDs and polynomial factorization will benefit from this speedup.

Computation of Risk Measures via Efficient Least-squares Monte Carlo

The computation of risk profiles for financial products and portfolios is an extremely important problem, both for regulatory and internal management purposes. For complex products whose value depends on a number of underlying risk factors and for which exercise decisions can be made prior to maturity, Monte Carlo simulation techniques are the only viable procedures. This project aims to adopt a simulation method used for pricing products, to computing risk exposures. Various ways of improving the computational speed will be explored.

A Foundational Mathematics Course: Design, Implementation and Evaluation

This project will produce material, in the form of lesson plans, instructional guides and practice sheets, appropriate for a college-level foundational mathematics course and will monitor its effectiveness during an implementation at on Ontario college in the fall semester, 2009. Once completed, the material will become part of JUMP's growing body of course materials. It is hoped that the material will prove effective in addressing the mathematics requirement of college students and will be adopted at more institutions, fulfilling JUMP's goal of "[promoting] a numerate society".

A Population Modelling Tookit for First Nations Commercial Fisheries Management

The goal of this research project is to develop a management toolkit that will enable First Nation fisheries managers to select and employ appropriate mathematical population models based on management objectives and available data. The primary societal contribution of this research program is the development of a toolkit that will immediately enable access to ecological risk assessment (ERA) tools that target the appropriate level of biological organization (i.e. populations) in a transparent, accountable, and scientifically defensible manner.

Development of a Dynamic Model for In Vitro DNA Ligand Selection

Aptamers are single stranded DNA molecules that due to their sequence bind to specific target molecules. The process for the identification of aptamers for a specific target involves exposure of a large number of random sequences to the target followed by selection of sequences that bind. This process requires several several selection cycles for success. Selection is based on two overlapping factors, strengh of binding and specificity of binding.

An Inverse Gaussian plume approach for estimating zinc emissions from a smelting operation.

Teck Metals Ltd. operates one of the world’s largest integrated lead-zinc smelting operations out of Trail, British Columbia. Every year, they report on atmospheric emissions of zinc and other contaminants through Environment Canada’s National Pollutant Release Inventory (NPRI). The purpose of this internship is to extend an existing inverse Gaussian plume model for estimating the emissions of zinc from point sources. The input to the algorithm is a collection of measurements of particulate material deposited on the ground in the area around the Trail smelter.

Investigation of Methodologies for Counterparty Credit Risk and Credit Value Adjustment Calculation

The research project is to investigate a multi]factor multi]asset extension of the Hestonf93 stochastic volatility model for comprehensive Credit Value Adjustment calculation and Commodity Counterparty Credit Risk methodology. The extended model covers counterparty hazard rates correlated with the underlying and interest rates in order to model wrong]way exposure.

Automated Market Making

Catalyst Equities is a proprietary day trading firm, which means that they trade stocks with financing arranged by a third party. Currently, trades are made independently by members of the team with some dialogue over projections and decision criteria. In the future, partners want to expand their business to include automated trading, which they have past experience with.

Detection of Unexploded Ordnances: Magnetostriction due to Shock Demagnetization

Detection of unexploded ordnances (UXO), or munitions, has many humanitarian benefits. In order to uncover and remove them from an area, their magnetic properties are exploited using a technique to detect them called magnetometry. In order to separate the hazardous UXO from other harmless debris, the proposed project with Sky Research will deal with modeling their magnetic signature and how it changes from the time they are fired, to the time when they penetrate the ground with an impact force.

Support Implementation of Kamakura Risk Management System

For this project, the mathematical finance intern will assist in the development and implementation of a new Economic Capital system, a method used by society to produce and distribute goods and services. The internship will also look into the development and implementation of appropriate risk management policies and procedures. The intern will manage the performance of operational tasks related to asset and liability compliance reporting and credit reporting as well as oversee the performance of credit and financial assessments of treasury credit counterparties.