### Abstracts

**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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