Skip to main content
Ontario Tech acknowledges the lands and people of the Mississaugas of Scugog Island First Nation.

We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

Learn more about Indigenous Education and Cultural Services

April 1, 2015

Speaker: Justin Wan, University of Waterloo

Title: Numerical Methods for Linear and Nonlinear Problems in Computational Finance and Economics

Abstract: In this talk, we will present accurate and efficient numerical methods for solving linear and nonlinear problems in the areas of computational finance and economics which give rise to interesting partial differential equations (PDEs) that show similarity to traditional PDE problems but also possess unique characteristics of its own. For instance, option pricing based on the standard Black-Scholes model leads to a heat equation, convection dominated problem, and a linear complementarity problem for the European, Asian and American option, respectively. The jump-diffusion model, which captures jumps in asset prices, yields a partial integro-differential equation (PIDE). Recently, the more sophisticated financial models were formulated as optimal stochastic control problems, which can be written as nonlinear Hamilton-Jacobi-Bellman equations (one control) and Hamilton-Jacobi-Bellman-Issac equations (two controls). These non-standard PDEs give rise to new challenges to designing fast solvers.

In this talk, we will present accurate and efficient numerical methods for solving linear and nonlinear equations in finance and economics. We will also present theoretical analysis to justify the numerical techniques. Numerical results will be given for a variety of equations arising from financial and economic modeling.