The term structure of interest rates
Topic
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.
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.
Speakers
Additional Information
Probability Seminar 2007
Ivar Ekeland (University of British Columbia)
Ivar Ekeland (University of British Columbia)