## The term structure of interest rates

- Date: 02/07/2007

Ivar Ekeland (University of British Columbia)

University of British Columbia

The interest rate r(t,t+x) between time t and time t+x is a smooth function of x, say

ho_t(x). We consider

ho_t as a stochastic process on (0,infty) into a suitable Hilbert space

of curves, and we seek to define it as the solution of an appropriate

equation, relying on accepted financial modelling. Unfortunately, this

equation is not a SDE, for the right-hand term contains an unbounded

operator on the Hilbert space, namely the derivative d/dx. We show in

what sense this equation has a solution, we apply the result to optimal

portfolio management, and if time permits we will touch upon the

existence of finite-dimensional realizations.

Probability Seminar 2007