Optimal stopping in Hilbert spaces and pricing of American options

We consider an optimal stopping problem for a Hilbert-space valued diffusion. We prove that the value function of the problem is the unique viscosity solution of an obstacle problem for the associated parabolic partial differential equation in the Hilbert space. The results are applied to investigate the pricing of American interest rate options in the lognormal Heath-Jarrow-Morton model of yield curve dynamics. Key words. Optimal stopping, obstacle problems, viscosity solutions, option pricing. AMS Subject Classification. 35R20, 49L25, 90A09, 49J15, 60H10. 1 Introduction Optimal stopping problems in finite dimensional domains and obstacle partial differential equations associated with them have been studied extensively in the past. Classical results Andrzej ' Swi¸ech was partially supported by NSF grant DMS-9706760 on the subject can be found in [2],[1]. In recent years the field of stochastic optimal control has developed significantly due to the introduction of the notion of ..