July 17, 2024

Seminar Series on Quantitative Finance - January 28, 2004


Ivar Ekeland, Director, Pacific Institute for the Mathematical Sciences
Managing bond portfolios
We present a Hilbertian framework for studying the term structure of interest rates, with infinitely many sources of risk. Applications are given to managing bond portfolios, and some explicit formulas are provided. This is joint work with Erik Taflin.

Agnes Tourin, Department of Mathematics and Statistics, McMaster University
Numerical schemes for Hamilton-Jacobi-Bellman equations arising in mathematical finance
Many problems arising in Finance, such as Portfolio Selection, are adequately modelled by the theory of stochastic control. It is often convenient to solve the problem by approximating numerically the Hamilton-Jacobi-Bellman equation characterizing the optimal policies. In some situations, for instance, in presence of singular control, it is the only robust method available. Finite difference schemes for Variational Inequalities arising in Finance will be discussed. In particular, I will explain how the exploitation of several kinds of operator splitting methods lead to simple numerical schemes. A particular application will be presented.

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