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.

Other Information: 

Probability Seminar 2007